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Syllabus
30. Using the measurements given in figure alongside,
(a) find the values of :
(1) sin (ii) tan .
(b) write an expression for AD in terms of .
Hint: (b) CD = 5. Draw DE perpendicular to AB, BE = 5, EA = 9.
Q.37. In the following figure, AB = 4 cm and ED = 3 m.
If find the length of BD.
(a) 2 (b) 1 (c) 0 (d) None of these.
(xxii) If tan + cot = 2, then the value of tan - cot is
(a) 1 (b) 2 (c) - 1 (d) None of these.
(xxiii) If 3 cos - 4 sin = 5, then the value of 3 sin + 4 cos is
(a) 1 (b) 2 (c) 0 (d) None of these.
i) cos angle CBD
ii) cot angle ABD
Experts, please answer this question as soon as possible along with the explanation.
Thank you.
In a triangle ABC
Angle b = 90 degrees
Sin a = 8/11
Show that
1.sec squareA-tan square A = 1
2.cot square A-cosec square A+1 = 0
7. Find AB.
Tan2θ/ (sec2θ-1)2 = 1+ cosθ/(1- cos θ)
Q12. If
Q13. If
Q14. If
Fast
Q12. Without using trigonometrical tables, evaluate :
(i) (ii)
(iii) sin234° + sin256° + 2 tan 18° tan 72° – cot2 30°.
Q13. Prove the following :
(i)
(ii) cos
(iii) .
Q14. Prove the following :
(i)
(ii)
Q15. Simplify the following :
(i)
2. If tan = cot and , State the value of .
3. If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
8 (c) In the figure (3) given below, AD is perpendicular to BC, BD=15 cm, sin B= and tan C=1
(i) Calculate the lengths of AD, AB, DC and AC.
1. (Cos 13 + sin 13)/ (cos 13 - sin 13) = tan A
What is A?
2. (sin 20 cos 70 + cos 20 sin 70)/ (sin 23 cosec 23 + cos 23 sec 23)= ?
3. If tan a = 5/6 and tan b = 1/11, then what is the value of a + b ?
EVALUATE THE FOLLOWING EXPRESSION WITHOUT USING TRIGONOMETRIC TABLES-
cot 30/ sec 30 + cosec 30/ tan 45 - cos245 + 2cos0/sin30
Cot^2 a (sec a -1/1+ sin a)
+ Sec^2 a (sin a -1/1+ sec a)=0?
2 sin X= a+ 1/a is true?
(i) sin A (ii) cos A (iii) tan C
Then prove that cos^8x+sec^8x=2
If x = 15 degrees , evaluate
4 cos 2x.sin 4x.tan 3x-1
Example.1. If a = cos 2 and b = sin 7, then
(a) a > 0, b > 0
(b) ab < 0
(c) a > b
(d) a < b