SSC CGL MOST PROBABLE - TRIGONOMETRY QUIZ- 13

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.

$1 \frac{1}{4}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

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. } $

$\frac{32}{3}$

$\frac{2}{3}$

$\frac{33}{99}$

$\frac{8}{3}$

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.

$\frac{2 \sqrt{3}+1}{5}$

1

$\frac{3}{5}(1+2 \sqrt{3})$

$\frac{2}{5}(1+\sqrt{3})$

Question 4:

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

$\operatorname{cosec}^{6} \theta$

$\cos ^{4} \theta$

$\sin ^{6} \theta$

$\sec ^{4} \theta$

Question 5:

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

$23.5$

$44.5$

$43.5$

$41.5$

Question 6:

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

$\frac{5}{6}$

$\frac{6}{7}$

$\frac{7}{6}$

$\frac{8}{3}$

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 $\mathrm{a}+\frac{b}{c}+\mathrm{d}$

4

0

1

3

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.

$150(\sqrt{3}+1)$

$200(\sqrt{3}+1)$

$50(3+\sqrt{3})$

$50(\sqrt{3}+1)$

Question 9:

In the given figure, find the area?

$\frac{135 \sqrt{3}}{4}$

$\frac{145 \sqrt{3}}{4}$

$\frac{120 \sqrt{3}}{7}$

$\frac{145 \sqrt{5}}{7}$

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 $\mathrm{AD}=$ ?