Page No 339:
Question 1:
Without using trigonometric tables, evaluate:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
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Question 2:
Prove that:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Answer:
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Question 3:
Without using trigonometric tables, evaluate:
(i)
(ii)
(iii)
(iv)
Answer:
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Question 4:
Without using trigonometric tables, prove that:
(i) cos 81° − sin 9° = 0
(ii) tan 71° − cot 19° = 0
(iii) cosec 80° − sec 10° = 0
(iv) cosec272° − tan218° = 1
(v) cos275° + cos215° = 1
(vi) tan266° − cot224° = 0
(vii) sin248° + sin242° = 1
(viii) cos257° − sin233° = 0
(ix) (sin 65° + cos 25°)(sin 65° − cos 25°) = 0
Answer:
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Question 5:
Without using trigonometric tables, prove that:
(i) sin53° cos37° + cos53° sin37° = 1
(ii) cos54° cos36° − sin54° sin36° = 0
(iii) sec70° sin20° + cos20° cosec70° = 2
(iv) sin35° sin55° − cos35° cos55° = 0
(v) (sin72° + cos18°)(sin72° − cos18°) = 0
(vi) tan48° tan23° tan42° tan67° = 1
Answer:
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Question 6:
Prove that:
(i) tan5° tan25° tan30° tan65° tan85° =
(ii) cot12° cot38° cot52° cot60° cot78° =
(iii) cos15° cos35° cosec55° cos60° cosec75° =
(iv) cos1° cos2° cos3° ... cos180° = 0
(v)
Answer:
Disclaimer: The RHS of (v) given in textbook is incorrect. There should be 2 instead 1. The same has been corrected in the solution here.
Page No 341:
Question 7:
Prove that
(i) sin (70° + θ) − cos (20° − θ) = 0
(ii) tan (55° − θ) − cot (35° + θ) = 0
(iii) cosec (67° + θ) − sec (23° − θ) = 0
(iv) cosec (65 °+ θ) sec (25° − θ) − tan (55° − θ) + cot (35° + θ) = 0
(v) sin (50° + θ ) − cos (40° − θ) + tan 1° tan 10° tan 80° tan 89° = 1.
Answer:
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Question 8:
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
(i) sin67° + cos75°
(ii) cot65° + tan49°
(iii) sec78° + cosec56°
(iv) cosec54° + sin72°
Answer:
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Question 9:
If sin 3 A = cos (A − 26°), where 3 A is an acute angle, find the value of A.
Answer:
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Question 10:
If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.
Answer:
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Question 11:
If sec 4 A = cosec (A − 15°), where 4 A is an acute angle, find the value of A.
Answer:
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Question 12:
If A, B, C are the angles of a ΔABC, prove that tan () = cot .
Answer:
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Question 13:
Answer:
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Question 14:
Answer:
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Question 15:
Prove that:
Answer:
Hence Proved
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Question 16:
Answer:
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Question 17:
Answer:
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Question 18:
Answer:
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Question 19:
tan 7° tan 23° tan 60° tan 67° tan 83° + + sin 20° sec 70° − 2
Answer:
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Question 20:
(sin225° + sin265°) + (tan 5° tan 15° tan 30° tan 75° tan 85°)
Answer:
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Question 21:
Answer:
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Question 22:
Answer:
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Question 23:
Answer:
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Question 24:
Answer:
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Question 25:
Answer:
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Question 26:
Answer:
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Question 27:
Answer:
Page No 343:
Question 1:
(a)
(b)
(c)
(d) 1
Answer:
(d) 1
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Question 2:
(a) 0
(b) 1
(c) 2
(d) None of these
Answer:
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Question 3:
(a) 1
(b) 2
(c)
(d) 8
Answer:
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Question 4:
cos 1° cos 2° cos 3° ... cos 180° = ?
(a) −1
(b) 1
(c) 0
(d)
Answer:
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Question 5:
tan 10° tan 15° tan 75° tan 80° = ?
(a)
(b)
(c) −1
(d) 1
Answer:
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Question 6:
tan 1° tan 2° tan 3° ... tan 89° = ?
(a) 1
(b) 0
(c) Cannot be determined
(d) None of these
Answer:
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Question 7:
tan 5° tan 25° tan 30° tan 65° tan 85° = ?
(a)
(b)
(c) 1
(d) none of these
Answer:
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Question 8:
cot 15° cot 16° cot 17° ... cot 73° cot 74° cot 75° = ?
(a)
(b) 0
(c) 1
(d) −1
Answer:
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Question 9:
(a)
(b)
(c) 2
(d) 3
Answer:
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Question 10:
(sin 40° − cos 50°) = ?
(a) sin 10°
(b) cos 10°
(c) 1
(d) 0
Answer:
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Question 11:
(cos237° − sin253°) = ?
(a)
(b)
(c) 1
(d) 0
Answer:
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Question 12:
(sin 43°cos 47° + cos 43°sin 47°) = ?
(a) sin 4°
(b) cos 4°
(c) 1
(d) 0
Answer:
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Question 13:
(a) 1
(b) 0
(c) −1
(d) Cannot be calculated
Answer:
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Question 14:
(sin 79° cos 11° + cos 79° sin 11°) = ?
(a)
(b)
(c) 0
(d) 1
Answer:
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Question 15:
(a) 3
(b) 2
(c) 1
(d) 0
Answer:
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Question 16:
(a)
(b)
(c) 2
(d)
Answer:
(b)
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Question 17:
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
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Question 18:
(cosec257° − tan233°) = ?
(a) 0
(b) 1
(c) 2
(d) None of these
Answer:
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Question 19:
(cos228° − sin262°) = ?
(a) 0
(b) 1
(c) 2
(d) None of these
Answer:
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Question 20:
(sec210° − cot280°) = ?
(a) 1
(b) 0
(c)
(d) None of these
Answer:
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Question 21:
cos (40° + θ) − sin (50° − θ) = ?
(a) 1
(b) 0
(c) sin 2θ
(d) None of these
Answer:
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Question 22:
sin (45° + θ) − cos (45° − θ) = ?
(a) 2 sin θ
(b) 2 cos θ
(c) 0
(d) 1
Answer:
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Question 23:
cosec (75° + θ) −sec (15° − θ) = ?
(a) 2 sec θ
(b) 2 cosec θ
(c) 0
(d) 1
Answer:
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Question 24:
If sin (θ + 34°) = cos θ and θ is acute, then θ = ?
(a) 56°
(b) 66°
(c) 28°
(d) 42°
Answer:
(d) 42°
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Question 25:
sin θ cos (90° − θ) + cos θ sin (90° − θ) = ?
(a) 0
(b) 1
(c) 2
(d)
Answer:
(b) 1
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Question 26:
(a)
(b)
(c)
(d)
Answer:
(c)
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Question 27:
If sin 3A = cos (A − 10°), where 3A is an acute angle, then ∠A = ?
(a) 35°
(b) 25°
(c) 20°
(d) 45°
Answer:
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Question 28:
If tan 2A = cot (A − 21°), where 2A is an acute angle, then ∠A = ?
(a) 24°
(b) 27°
(c) 35°
(d) 37°
Answer:
(d) 37°
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Question 29:
If sec 5A = cosec (A − 30°), where 5A is an acute angle, then ∠A = ?
(a) 35°
(b) 25°
(c) 20°
(d) 27°
Answer:
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Question 30:
If A and B are acute angles such that sin A = cos B, then (A + B) = ?
(a) 45°
(b) 60°
(c) 90°
(d) 180°
Answer:
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Question 31:
sec 70° sin 20° + cos 20° cosec 70° = ?
(a) 0
(b) 1
(c) −1
(d) 2
Answer:
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Question 32:
cot (90° − θ) = ?
(a) cot θ
(b) −cot θ
(c) tan θ
(d) −tan θ
Answer:
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Question 33:
If cos 9 α = sin α and 9α < 90°, then tan 5 α = ?
(a)
(b)
(c) 1
(d) 0
Answer:
(c) 1
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Question 34:
If cos(α + β) = 0, then sin(α − β) = ?
(a) sin α
(b) cos β
(c) sin 2α
(d) cos 2β
Answer:
(d) cos 2β
Page No 348:
Question 1:
(a)
(b) 4
(c) 6
(d) 5
Answer:
(b) 4
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Question 2:
The value of
(a)
(b)
(c) 6
(d) 2
Answer:
(d) 2
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Question 3:
If cos A + cos2 A = 1, then (sin2 A + sin4 A) = ?
(a)
(b) 2
(c) 1
(d) 4
Answer:
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Question 4:
If sin , then (cosec θ + cot θ) = ?
(a)
(b)
(c)
(d)
Answer:
(d)
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Question 5:
If cot , prove that
Answer:
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Question 6:
If 2x = sec A and = tan A, prove that
Answer:
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Question 7:
If tan θ = 3 sin θ, prove that (sin2 θ − cos2 θ) =
Answer:
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Question 8:
Prove that
Answer:
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Question 9:
If 2 sin 2θ =, prove that θ = 30°.
Answer:
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Question 10:
Prove that = (cosec A + cot A).
Answer:
= (cosec A + cot A).
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Question 11:
If cosec θ + cot θ = p, prove that cos θ =
Answer:
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Question 12:
Prove that (cosec A − cot A)2 =
Answer:
(cosec A − cot A)2 =
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Question 13:
If 5 cot θ = 3, find the value of
Answer:
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Question 14:
Prove that (sin 32° cos 58° + cos 32° sin 58°) = 1.
Answer:
(sin 32° cos 58° + cos 32° sin 58°) = 1
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Question 15:
If x = a sin θ + b cos 0 and y = a cos 0 b sin θ, prove that
Answer:
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Question 16:
Prove that = (sec θ + tan θ)2.
Answer:
= (sec θ + tan θ)2
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Question 17:
Prove that .
Answer:
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Question 18:
Prove that
Answer:
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Question 19:
Prove that
Answer:
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Question 20:
If sec 5 A = cosec (A − 36) and 5 A is an acute angle, find the value of A.
Answer:
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