The number of non - similar isosceles satisfying the equation $\tan A+\tan B+\tan C=100$, where $A,B \& C$ are angles of any one of the triangles are

If $\cos \theta =\frac{2p}{p^2+1}$, $\left(p\ne \pm 1\right)$ then $\mathrm{cosec}\theta$ is equal to:

If $\sin \theta =\frac{1}{\sqrt{2}}$, then $(\tan \theta + \cos \theta )$ = 

1. $\frac{1}{\sqrt{2}}$
2. $\frac{2}{\sqrt{2}}$ 
3. $\frac{3}{\sqrt{2}}$
4. $\frac{(1+\sqrt{2})}{\sqrt{2}}$

The value of $(\sin \theta + \cos \theta {)}^2=?$

1. $1+{\sin }^2\theta$
2. ${\sin }^2\theta +{\cos }^2\theta$ 
3.$1+2 \cos \theta \sin \theta$ 
4. ${\cos }^2 \theta + 1$

If $L={\sin }^2\left(\frac{\pi }{16}\right)-{\sin }^2\left(\frac{\pi }{8}\right)$ and $M={\cos }^2\left(\frac{\pi }{16}\right)-{\sin }^2\left(\frac{\pi }{8}\right)$

What is the value of ${\cos }^{2}5°+{\cos }^{2}10°+ \_\_\_\_\_+{\cos }^{2}90°$