CDS MATHEMATICS TRIGONOMETRY QUIZ 24

Question 1:

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 2:

If $1+\sin \theta+\sin ^{2} \theta+\ldots \ldots \infty=4+2 \sqrt{3}$ then find the value of ' $\theta$ '

$30^{\circ}$

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

Question 3:

If $\cos 43^{\circ}=\frac{x}{\sqrt{x^{2}+y^{2}}}$, then find the value of $\tan 47^{\circ}$ is.

$\frac{y}{x}$

$\frac{x}{y}$

$\frac{y}{\sqrt{x^{2}}+y^{2}}$

$x$.

Question 4:

find $\max ^{m}$ value of $\sin ^{8} \theta+\cos ^{14} \theta$?

1

2

–1

0

Question 5:

If $A, B, C$, And $D$ are the Angles of a Cyclic quadrilaterals then find $\cos A+\cos B+\cos C+cosD $= ?

1

2

0

-1

Question 6:

Let $\cos \alpha+\cos \beta=2$ and $\sin \alpha+\sin \beta=0$, where $0 \leq \alpha \leq 90^{\circ}, 0 \leq \beta \leq 90^{\circ}$. What is the value of $\cos 2 \alpha-\cos 2 \beta$ ?

0

1

2

Cannot be determined due to insufficient data

Question 7:

The value of $\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ}$ is equal to:

0

1

-1

2

Question 8:

Find the value.

$\frac{\tan 5 \theta+\tan 3 \theta}{4 \cos 4 \theta(\tan 5 \theta-\tan 3 \theta)}$

$\sin2\theta$

$\cos2\theta$

$\tan2\theta$

$\cot2\theta$

Question 9:

If $p=\sec \theta-\tan \theta$ and $q=\operatorname{cosec} \theta+\cot \theta$, then what is $p+q(p-1)$ equal to?

$-1$

$0$

$1$

$2$

Question 10:

Find the value.

$2 \sin ^{2} \beta+4 \sin (\alpha+\beta) \cdot \sin \alpha \cdot \sin \beta$ $+\cos 2(\alpha+\beta)$

$\sin 2 \beta$

$\cos 2 \alpha$

$\sin 2 \alpha$

$\cos 2 \beta$