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Question 1:

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

Question 2:

Find the value $\tan 2 x$.

Question 3:

If the sides of a triangle are three consecutive natural numbers and its greatest angle is twice the smallest angle, then the triangle will haves sides.

Question 4:

If $\tan \theta=\frac{x\sin \phi}{1-x \cos \phi}$ and $\tan \phi=\frac{y \sin \theta}{1-y \cos \theta}$ find the value of $\frac{x}{y}$ :

Question 5:

If $\tan m \theta=\operatorname{tan}n \theta$ then different value of $\theta$ :

Question 6:

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

Question 7:

If $\sin \theta=\cos ^{2} \theta$, find the value of $\cos ^{2} \theta(1+$ $\left.\cos ^{2} \theta\right)$ :

Question 8:

In an equilateral triangle, the relation between the inner radius and the out radius:

Question 9:

$\cos ^{2} \theta+\frac{1}{\operatorname{cosec}^{2} \theta}+17=x$. What is the value of $x^{2}$ ?

Question 10:

$\sin ^{2} \theta_{1}+\cos ^{2} \theta_{2}=1$ then what is the value of $\theta_{1} , \theta_{2} ?$