## Trigonometry Questions and Answers Part-1

1. If $3\sin \theta+4\cos \theta=5$    , then the value of $4\sin \theta-3\cos \theta$    is equal to
a) 3
b) 2
c) 1
d) 0

Explanation:

2. $\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+\sin^{2}39^{\circ}+\sin^{2}48^{\circ}-\sin^{2}9^{\circ}-\sin^{2}18^{\circ}$
is equal to
a) -1
b) 0
c) 1/2
d) 1

Explanation:

3. $\cos 2\alpha-2\sin^{2}\beta-4\cos \left(\alpha+\beta\right)\sin\alpha\sin\beta-\cos 2\left(\alpha+\beta\right)$
is independent of
a) $\alpha$
b) $\beta$
c) both $\alpha$ and $\beta$
d) none of these

Explanation:

4. If $\frac{\sin\theta}{\cos3\theta}+\frac{\sin3\theta}{\cos9\theta}+\frac{\sin9\theta}{\cos27\theta}=\frac{1}{2}\left(\tan x- \tan \theta\right)$
then the value of x is
a) $3\theta$
b) $6\theta$
c) $9\theta$
d) $27\theta$

Explanation:

5. If $2\sin \alpha\cos\beta\sin\gamma=\sin\beta\sin\left(\alpha+\gamma\right)$
then $\tan\alpha,\tan\beta,\tan\gamma$    are in
a) Arithmetic progression
b) Geometric progression
c) Harmonic progression
d) none of these

Explanation:

6. If $\cot\alpha+\tan\alpha=m$    and $\frac{1}{\cos\alpha}-\cos\alpha=n$     , then
a) $m\left(mn^{2}\right)^{1/3}-n\left(nm^{2}\right)^{1/3}=1$
b) $m\left(m^{2}n\right)^{1/3}-n\left(mn^{2}\right)^{1/3}=1$
c) $n\left(mn^{2}\right)^{1/3}-m\left(nm^{2}\right)^{1/3}=1$
d) $n\left(m^{2}n\right)^{1/3}-m\left(mn^{2}\right)^{1/3}=1$

Explanation:

7. If $a \cos ^{3}\alpha+3a\cos \alpha\sin^{2}\alpha =m$       and $a \sin ^{3}\alpha+3a\cos^{2} \alpha\sin\alpha =n$       , then $\left(m+n\right)^{2/3}+\left(m-n\right)^{2/3}$     is equal to
a) $2a^{2}$
b) $2a^{1/3}$
c) $2a^{2/3}$
d) $2a^{3}$

Explanation: From the given relations, we get

8. if $\frac{2 \sin \alpha}{1+\cos\alpha+\sin\alpha}=y$     , then $\frac{1-\cos\alpha+\sin\alpha}{1+ \sin \alpha}$     is equal to
a) 1/y
b) y
c) 1-y
d) 1+y

Explanation:

9. Minimum value of $4x^{2}-4x \mid \sin\theta\mid -\cos^{2}\theta$       is equal to
a) -2
b) -1
c) -1/2
d) 0

10. If $\sin\theta$   and $\cos\theta$  are the roots of the equation $ax^{2}-bx +c=0$    , then a, b and c satisfy the relation
a) $a^{2}+b^{2}+2ac=0$
b) $a^{2}-b^{2}+2ac=0$
c) $a^{2}+c^{2}+2ab=0$
d) $a^{2}-b^{2}-2ac=0$
Explanation: Since sin $\theta$ and cos $\theta$ are roots of the given