Here are some good Important trigonometry questions for class 11 Maths
1.if $tan \theta = \frac {a}{b}$ , show that $\frac {a sin \theta – b cos \theta}{a sin \theta + b cos \theta}= \frac {a^2 – b^2}{a^2 + b^2}$
2.Prove that $sec^4 x – sec^x = tan^4x + tan^2 x$
3.Prove that $cosec x ( sec x -1) – cot x(1- cos x) = tan x – sin x$
4.if $2C = A + B$, prove that
$cot B = \frac {sin A – sin C}{Cos C – CosA}$
5.Find the values of the below expression
a. $ cos 20^{\circ} cos 40^{\circ} cos 60^{\circ} cos 80^{\circ}$
b. $sin 10^{\circ} sin30^{\circ} sin 50^{\circ} sin70^{\circ}$
6.if $Sinx = \frac {3}{5} ,cos y=\frac {9}{41} , 0<x,y < \frac {\pi}{2}$, then find the values
a. sin (x -y)
b. tan (x-y)
c. cot (x+y)
7.Derive the values of the angle
a. $sin 18^{\circ}$
b. $tan15^{\circ}$
c. $sin 67 \frac {1}{2}^{\circ}$
8.Prove that
$cos 55^{\circ} + cos 65^{\circ} + cos175^{\circ}=0$
9. If $y = cos^2x + sin^4x$ for all values of x, then prove that
$ \frac {3}{4} \leq y \leq 1$
10.Find the solution of the trigonometric equation $2 tan^2 x + sec^2 x = 2$ in the range $[0,2\pi]$
11.Which of the following is not correct?
(A) sin A = –1/5
(B) cos A = 1
(C) sec A =1/2
(D) tan A = 20
12.Show that $2 sin^2 y + 4 cos (x + y) sin x sin y + cos 2 (x + y) = cos 2x$
Answer
5
a. 1/16
b. 1/16
6.
a. -133/205
b. -133/156
c. -84/187
7.
a. $\frac {\sqrt {5} -1}{4}$
b. $2- \sqrt {3}$
c.$\frac {\sqrt {2+ \sqrt {2}}}{2}$
10.$( \pi/6, 5\pi/6, 7 \pi/6 ,11 \pi/6)$
11.c
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