Page No 312:
Question 1:
Without using trigonometric tables, evaluate:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
Page No 312:
Question 2:
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:
Page No 313:
Question 3:
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:
Page No 313:
Question 4:
Prove that:
Answer:
Page No 313:
Question 5:
Prove that:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Answer:
Page No 313:
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 314:
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:
Page No 314:
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:
Page No 314:
Question 9:
If A, B and C are the angles of a ABC, prove that .
Answer:
Page No 314:
Question 10:
Answer:
Hence, the value of is
Page No 314:
Question 11:
If sec2A = cosec(A 42), where 2A is an acute angle, then find the value of A. [CBSE2008]
Answer:
We have,
Hence, the value of A is .
Page No 314:
Question 12:
If sin 3 A = cos (A − 26°), where 3 A is an acute angle, find the value of A.
Answer:
Page No 314:
Question 13:
If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.
Answer:
Page No 314:
Question 14:
If sec 4 A = cosec (A − 15°), where 4 A is an acute angle, find the value of A.
Answer:
Page No 314:
Question 15:
Prove that:
Answer:
Hence Proved
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