SSC MTS MATHS(TRIGONOMETRY) QUIZ

Question 1:

In the given figure, if $\mathrm{AB}=\mathrm{AC}=8 \mathrm{~cm}, \mathrm{BC}=$ $11 \mathrm{~cm}$ and $\mathrm{BD}=7 \mathrm{~cm}$, then find $\mathrm{AD}=$ ?

$6 \mathrm{~cm}$

$5.5 \mathrm{~cm}$

$4 \mathrm{~cm}$

$7 \mathrm{~cm}$

Question 2:

The equation $\cos 2 \theta+p \sin \theta=2 p-7$ has a solution

$2 \leq p \leq 6$

$\mathrm{p}>7$

$p \leq 1$

$0 \leq p \leq 1$

Question 3:

If $\alpha+\beta+\gamma=\alpha \beta \gamma$ ,then value of $\frac{\alpha}{1-\alpha^{2}} + \frac{\beta}{1-\beta^{2}}+\frac{\gamma}{1-\gamma^{2}}$ is

$\frac{4 \alpha \beta \gamma}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

$\frac{8 \alpha \beta \gamma}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

$\frac{4 \alpha^{2} \beta^{2} \gamma^{2}}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

$\frac{\alpha \beta \gamma}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

Question 4:

The maximum value of $\sin x+\cos x$ is:

1

$\sqrt{2}$

2

$1+\sqrt{2}$

Question 5:

Find the value $\cos ^{4}\left(\frac{\pi}{8}\right)+\cos ^{4}\left(\frac{3 \pi}{8}\right)+\cos ^{4}$ $\left(\frac{5 \pi}{8}\right)+\cos ^{4}\left(\frac{7 \pi}{8}\right)$

0

$\frac{1}{2}$

$\frac{3}{2}$

1

Question 6:

Find the value $\tan 2 x$.

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

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

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

None of these

Question 7:

If $(\sec \alpha+\tan \alpha)(\sec \beta+\tan \beta)(\sec \gamma+\tan \gamma)$ $=\tan \alpha\tan \beta \tan \gamma$, find the value of $(\sec \alpha-$ $\tan \alpha)(\sec \beta-\tan \beta)(\sec \gamma-\tan \gamma)$

$\tan \alpha+\tan \beta+\tan \gamma$

$\tan \alpha-\tan \beta-\tan \gamma$

$\cot \alpha+\cot \beta+\cot \gamma$

$\cot \alpha \cot \beta \cot \gamma$

Question 8:

$\frac{\sin A+\sin B}{\cos A-\cos B}+\frac{\cos A+\cos B}{\sin A-\sin B}=?$

$\sin A \cos B$

$\tan A \tan B$

0

$\cos A \cos B$

Question 9:

If $\sec A=\frac{41}{40}$, given that $A<90^{\circ}$, What is the value of the following?

$\frac{82 \sin A+9 \cot A}{164 \cos A-80 \tan A}$

$\frac{58}{142}$

$\frac{54}{142}$

$\frac{74}{147}$

$\frac{56}{124}$

Question 10:

If $3\left(\sec ^2 \theta+\tan ^2 \theta\right)=5,0^{\circ}<\theta<90^{\circ}$, then the value of $\operatorname{cosec} \theta$ is:

2

$ \frac{1}{3}$

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

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