# SSC CGL MOST PROBABLE - TRIGONOMETRY QUIZ- 13

Attempt now to get your rank among 2 students!

## Question 1:

The numerical value of $\frac{\cos ^{2} 45^{\circ}}{\sin ^{2} 60^{\circ}}+\frac{\cos ^{2} 60^{\circ}}{\sin ^{2} 45^{\circ}}-\frac{\tan ^{2} 30^{\circ}}{\cot ^{2} 45^{\circ}}-\frac{\sin ^{2} 30^{\circ}}{\cot ^{2} 30^{\circ}}$ is.

## Question 2:

The value of $\frac{\tan 30^{\circ} \operatorname{cosec} 60^{\circ}+\tan 60^{\circ} \sec 30^{\circ}}{\sin ^{2} 30^{\circ}+4 \cot ^{2} 45^{\circ}-\sec ^{2} 60^{\circ}} \text { is. }$

## Question 3:

If $7 \sin ^{2} \theta-\cos ^{2} \theta+2 \sin \theta=2, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{\sec 2 \theta+\cot 2 \theta}{\operatorname{cosec} 2 \theta+\tan 2 \theta}$ is.

## Question 4:

The value of $\frac{\tan ^{2} \theta-\sin ^{2} \theta}{2+\tan ^{2} \theta+\cot ^{2} \theta}$ is

## Question 5:

Find the value of $\frac{\tan 1^{\circ}}{1+\tan 1^{\circ}}+\frac{\tan 2^{\circ}}{1+\tan 2^{\circ}}+\ldots . .+\frac{\tan 89^{\circ}}{1+\tan 89^{\circ}}$

## Question 6:

If $\cos ^{4} \theta-\sin ^{4} \theta=\frac{2}{3}$, then find the value of $2 \cos ^{2} \theta-3 \sin ^{2} \theta=?$

## Question 7:

If $\cos A+\cos ^{2} A=1$ and $a \sin ^{12} A+b \sin ^{10} A+$ $c \sin ^{8} A+d \sin ^{6} A-1=0$. Find the vlaue of $\mathrm{a}+\frac{b}{c}+\mathrm{d}$

## Question 8:

In a triangle $A B C, A B=20 \mathrm{~cm}, \angle A B C=30^{\circ}$ and $\angle A C B=45^{\circ}$, Find the area of the triangle.

## Question 9:

In the given figure, find the area?

## Question 10:

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 $\mathrm{AD}=$ ?