$$ \text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y= $$

$$ \sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} \text { where } \theta \in\left[-\frac{\pi}{8}, \frac{\pi}{8}\right] \text { is equal to } $$

$$ \text { Value of } \cos 105^{\circ} \text { is } $$

$$ \text { If } \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta+\frac{2 \pi}{3}\right)}=\frac{z}{\cos \left(\theta-\frac{2 \pi}{3}\right)} \text { then } x+y+z \text { is equal to } $$

$$ \frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}= $$

$$ \left(\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\right)\left(\tan \frac{\pi}{12}+\cot \frac{\pi}{12}\right)= $$

If $$\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$$ then $$\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=$$

$$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }$$

$$ \text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)= $$

If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$ is equal to

The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as

$$ \cos ^6 A-\sin ^6 A \text { is equal to } $$

$$ \text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is } $$

If $$\cos \alpha=k \cos \beta$$ then $$\cot \left(\frac{\alpha+\beta}{2}\right)$$ is equal to

If $$\sin A+\sin B=a$$ and $$\cos A+\cos B=b$$, then $$\cos (A+B)$$ equals?

What is $${{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}$$ equal to?

If x and y are acute angles, such that $$\cos x + \cos y = {3 \over 2}$$ and $$\sin x + \sin y = {3 \over 4}$$, then $$\sin (x + y)$$ equals

The expression $${{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}$$ can be written as

$${\sin ^2}17.5^\circ + \sin 72.5^\circ $$ is equal to