SSC CGL QUANT QUIZ(TRIGONOMETRY)

Question 1:

If $\tan \theta=p/q$, then $\frac{p \sin \theta-q \cos \theta}{p \sin \theta+q \cos \theta}$ is equal to:

$\frac{p^{2}-q^{2}}{p^{2}+q^{2}}$

$\frac{p^{2}-q^{2}}{1 p q}$

$\frac{2 \mathrm{pq}}{\mathrm{p}^{2}-\mathrm{q}^{2}}$

$\frac{p^{2}+q^{2}}{p^{2}-q^{2}}$

Question 2:

Value of $2\left(\sin ^{6} \theta+\cos ^{6} \theta\right)-3\left(\sin ^{4} \theta+\cos ^{4} \theta\right)+1$ is:

1

2

4

0

Question 3:

If $\sec x+\cos x=3$, then $\tan ^{2} x-\sin ^{2} x$ is:

9

4

5

13

Question 4:

If $x=\sin \theta+\cos \theta$ and $y=\sec \theta+\operatorname{cosec} \theta$ find $y$ in terms of $x$.

$\frac{x}{x^{2}+1}$

$\frac{x}{x^{2}-1}$

$\frac{2 x}{x^{2}-1}$

$\frac{2 x}{x^{2}+1}$

Question 5:

If $\tan \theta \cdot \cos 60^{\circ}=\frac{\sqrt{3}}{2}$, then the value of $\sin \left(\theta-15^{\circ}\right)$ is:

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

$\frac{1}{2}$

1

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

Question 6:

If $\operatorname{Cot} x=\frac{5}{12}$, then $\operatorname{Sin} x+\frac{1}{\operatorname{Cot} x}+\operatorname{Sec} x=?$

$\frac{173}{13}$

$\frac{77}{13}$

$\frac{75}{13}$

$\frac{17}{13}$

Question 7:

If $\sin \left(\theta+18^{\circ}\right)=\cos 60^{\circ},\left(0^{\circ}<\theta<90^{\circ}\right)$ then value of $\cos 5 \theta$ is:

0

1

$\frac{1}{2}$

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

Question 8:

What is the value of $\frac{[(\cos 8 A+\cos 4 A)]}{(\sin 8 A-\sin 4 A)}$

$\cot \mathrm{A}$

$\cot 2 \mathrm{~A}$

$\cot 4 \mathrm{~A}$

$\tan 2 \mathrm{~A}$

Question 9:

If $r \sin \theta=\frac{9}{2}$ and $r \cos \theta=\frac{9 \sqrt{3}}{2}$ the value of $r$ is:

8

9

5

7

Question 10:

The value of $\sin 120^{\circ} \cos 330^{\circ}+\cos 240^{\circ} \sin 330^{\circ}$ is?

$-1$

$1$

$0$