Exercise 1

In triangle $ABC, \cos A+2\cos B+\cos C=2$, then-

If $\left(3-4{\sin }^{2}1\right)\left(3-4{\sin }^{2}3\right)\left(3-4{\sin }^2{3}^2\right)\dots \dots \left(3-4{\sin }^2\left(3^{n-1}\right)\right)=\sin a/\sin b$, where $n\in N \text{and} a, b$ are integers in radian, then the digit at the unit place of $(a+b)$ may be-

Find the exact value of ${\tan }^2\frac{\pi }{16}+{\tan }^2\frac{3\pi }{16}+{\tan }^2\frac{5\pi }{16}+{\tan }^2\frac{7\pi }{16}$.

If  $\sin \theta +\sqrt{\sin \theta +\sqrt{\sin \theta +\sqrt{\sin \theta +\dots \dots \infty }}}={\sec }^4\alpha$, then $\sin \theta$ is equal to -

If $\tan \frac{\theta }{2}=cosec\theta -\sin \theta$, then -

If $2\tan 10°+\tan 50°=2x, \tan 20°+\tan 50°=2y, 2\tan 10°+\tan 70°=2w$ and $\tan 20°+\tan 70°=2z$, then which of the following is/are true -

Let $A,B,C$ are $3$ angles such that $\cos A+\cos B+\cos C=0$ and if $\cos A\cos B\cos C=\lambda (\cos 3A+\cos 3B+\cos 3C)$, then $\lambda$ is equal to -

The angles $A, B, C$ of a triangle $ABC$ satisfy $4\cos A\cos B+\sin 2A+\sin 2B+\sin 2C=4$. Then which of the following statements is/are correct?