SSC TRIGONOMETRY QUIZ 11

Question 1:

If $3+\cos ^{2} \theta=3\left(\cot ^{2} \theta+\sin ^{2} \theta\right), \mathrm{O}<\theta<90^{\circ}$ then $(\cos \theta+2 \sin \theta) =?$

$3 \sqrt{2}$

$\frac{3+\sqrt{2}}{2}$

$\frac{2 \sqrt{3}+1}{2}$

$\frac{3 \sqrt{3}+1}{2}$

Question 2:

If $\operatorname{cosec} \theta, \sec \theta$ and $\cot \theta$ in G.P. then find $\tan ^{4} \theta+\sin ^{2} \theta=?$

0

1

$-1$

2

Question 3:

Find the value of trigonometic ratios:

$\cos \left(\frac{-25 \pi}{4}\right) ?$

1

0

$\frac{-1}{\sqrt{2}}$

$\frac{1}{\sqrt{2}}$

Question 4:

IF $\cos (\alpha+\beta)=0$ then find the value of $\tan (5 \alpha+6 \beta)$

$\tan \alpha$

$-\cot \beta$

$\tan \beta$

$-\cot \alpha$

Question 5:

If $\tan ^{2} \theta=1-e^{2}$ then find $\sec \theta+\tan ^{3} \theta \cdot \operatorname{cosec} \theta$?

$\left(2-e^{2}\right)^{3 / 2}$

$\left(2-e^{2}\right)^{1 / 2}$

$\left(1-e^{2}\right)^{1 / 2}$

$\left(1+e^{2}\right)^{5 / 2}$

Question 6:

If $a^{2} \sin ^{2} x+b^{2} \cos ^{2} x=c^{2}$ then find $2 \sin ^{2} x-$ $\cos ^{2} x ?$

$\frac{3 c^{2}-2 b^{2}-a^{2}}{a^{2}-b^{2}}$

$\frac{3 c^{2}-2 b^{2}-a^{2}}{a^{2}+b^{2}}$

$\frac{c^{2}-2 b^{2}+a^{2}}{a^{2}-b^{2}}$

$\frac{c^{2}-b^{2}+a^{2}}{a^{2}-b^{2}}$

Question 7:

Direction: Convert each of the following degree measure to radian measure.
$-90^{\circ}$

$\pi / 2$

$-\pi / 2$

$-3 \pi / 2$

$-\pi / 6$

Question 8:

If $p=\sin ^{2} \theta+\cos ^{4} \theta$ for $0 \leq \theta \leq \frac{\pi}{2}$, then consider the following statements :

1. $p$ can be less than $\frac{3}{4}$.

2. $p$ can be more than 1 .

Which of the above statements is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

Question 9:

If $\cos ^{n} \theta+\sec ^{n} \theta=2$, then $\cos ^{3} \theta+\sec ^{3} \theta=?$

1

4

0

2

Question 10:

If $\sin \theta+\sin ^{2} \theta=1$ then $\cos ^{12} \theta+3 \cos ^{10} \theta+3$ $\cos ^{8} \theta+\cos ^{6} \theta+1=?$

1

0