Trigonometric F...

If $$\alpha cos^23\theta +\beta cos^4\theta= 16 cos^6\theta + 9 cos^2\theta$$ is an identity then-

If $$\sin \left( {\pi \cos x} \right) = \cos \left( {\pi \sin x} \right)$$, then $$\sin 2x = $$

If $$x \in (\pi, 2\pi)$$ and $$\cos x + \sin x = \dfrac{1}{2}$$, then the value of $$\tan x$$ is

If $$\dfrac{{\left( {1 - \cos A} \right)}}{2} = x$$ then find the value of x is

If  $$x=\dfrac{{2\left( {\sin {1^0} + \sin {2^0} + \sin {3^0} + ....... + \sin {{89}^0}} \right)}}{{2\left( {\cos {1^0} + \cos {2^0} + .............\cos {{44}^0}} \right) + 1}}$$ , then the value of $${\log_x}2$$ is equal

A flag staff on the top of the tower $$80\ meter$$ high, subtends an angle $$\tan^{-1}\left(\dfrac{1}{9}\right)$$ at point on the ground $$100\ meters$$ away from the foot of the tower. Find the height of the flag-staff.

Total number of solution of the equation $$3x+2\tan x=\dfrac {5\pi}{2}$$ in $$x\ \epsilon [0,2\pi]$$ is equal to

$$\sin^{-1}x+\sin^{-1}\dfrac{1}{x}+\cos^{-1}x+\cos^{-1}\dfrac{1}{x}, x\notin \pm 1$$ is equal to?

Find  $$\dfrac{\sin^2A-\sin^2B}{\sin A\cos A-\sin B\cos B}=?$$.

If $$\tan\theta=\dfrac{a}{b}$$ then $$\dfrac{a\sin\theta-b\cos\theta}{a\sin\theta +b\cos\theta}=$$