SSC MATHEMATICS TRIGONOMETRY QUIZ 9

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Question 1:

Find the value

$\frac{\sin 30^{\circ}+\tan 45^{\circ}-\operatorname{cosec} 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$?

Question 2:

Find the value.

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

Question 3:

If $\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=\frac{4}{\sqrt{3}}, 0^{\circ}<\theta<90^{\circ}$ then find the value of $(\tan \theta+\sec \theta)^{-1}$.

Question 4:

If $A, B, C$ are the Angles of the a $\Delta$. then $\sin ^{2} \frac{A}{2}$ $+\sin ^{2} \frac{B}{2}+\sin ^{2} \frac{C}{2}+\sin ^{2} \frac{A+B}{2}+\sin ^{2} \frac{B+C}{2}+\sin ^{2} \frac{C+A}{2}=?$

Question 5:

Find the value of $\tan ^{n} 1^{\circ} \tan ^{n} 2^{\circ} \tan ^{n} 3^{\circ} \ldots \tan ^{n} 88^{\circ} \tan ^{n} 89^{\circ}$.

Question 6:

Find the value

$\tan 20^{\circ}+\tan 40^{\circ}+\sqrt{3} \tan 20^{\circ} \cdot \tan 40^{\circ}$

Question 7:

Consider the following inequalities :
1. $\sin 1^{\circ}<\cos 57^{\circ}$
2. $\cos 60^{\circ}>\sin 57^{\circ}$
Which of the above is/are correct?

Question 8:

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

Question 9:

Find $\max ^{m}$ value of $\sin ^{4} \theta \cdot \cos ^{4} \theta$?

Question 10:

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.

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