Trigonometric F...

If $$2\sin^2\theta -5\sin \theta +2 > 0, \theta \in (0, 2\pi)$$, then $$\theta \in$$

If $$0\leq x\leq \pi$$ and $$81^{\sin^2x}+81^{\cos^2x}=30$$, then x is equal to.

Solve: $$2(\cos x+\cos 2x)+\sin 2x(1+2\cos x)=2\sin x, -\pi \leq x \leq \pi$$.

Solve $$\tan \theta +\sec \theta =\sqrt{3}; 0\leq \theta \leq 2\pi$$.

A balloon is observed simultaneously from three points A B and C, on a straight road directly under it. The angular elevation at B is twice of what it is at A and the angular elevation at C is thrice of what it is at A. If the distance between A and B is 200 meters and the distance between B and C is 100 meters, then find the height of the balloon.

If $$P\left( 4 \right) = 3$$ and $$\displaystyle {\sin ^6}x + {\cos ^6}x = {a \over b}\left( {a,b \in N} \right)$$ and $$a,b$$ are relatively prime, then $$a + b$$ is equal to

The equation $${\sin ^6}x + {\cos ^6}x = {a^2}$$ has real solution if 

If $$\sec A + \tan A = m $$ and $$ \sec A - \tan A = n$$, find the value of $$\sqrt{mn}$$.

The most general value of $$\theta $$ satisfying both the equations $$\sin \theta  = \frac{1}{2},\tan \theta  = \frac{1}{{\sqrt 3 }}\;is\;\left( {n \in I} \right)$$ 

The expression $$\dfrac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}}$$ reduces to :