Trigonometric F...

If $$\sec$$ $$\beta=\alpha+\dfrac{1}{4a}$$,then the value of $$\sec\beta+\tan\beta$$ is

$$|\tan\theta+\sec\theta|=|\tan\theta|+|\sec\theta|, 0\leq \theta \leq 2\pi$$  is possible only if-

The sum of the solution of $$x$$ is-

The value of $$\displaystyle \sin ^{2}1^{\circ}+\sin ^{2}2^{\circ}+\sin ^{2}2^{\circ}+...+\sin ^{2}89^{\circ}+\sin ^{2}90^{\circ}$$

The total number of solutions of $$\displaystyle \sin \left \{ x \right \}=\cos \left \{ x \right \}$$ (where $$\displaystyle  \left \{ . \right \}$$ denotes the fractional part) in $$\displaystyle  \left [ 0,2\pi  \right ]$$ is equal to

The number of real solutions of $$\sin e^{x}.\cos e^{x}=2^{x-2}+2^{-x-2}$$ is