Trigonometric F...

$$(\cos A + \sin A)^2 - (\cos A - \sin A)^2$$ is equal to

If $$\alpha + \beta =90^0$$ and $$\alpha = 2\beta,$$ then $$\cos^2 \alpha + \sin^2 \beta$$ equals to

Total number of solution of $$\sin x=x+\dfrac {1}{x} x\epsilon (0, 2\pi)$$, is equal to-

If $$\sin$$$$\beta=\dfrac{12}{13},$$then the value of $$\dfrac{13\sin\beta+5 \sec\beta}{5\tan\beta+6 \csc\beta}$$

Th value of $$(\sin \theta + \csc \theta)^2 + (\cos\theta + \sec \theta)^2 - (\tan^2 \theta+\cot^2 \theta)$$ is

If $$\tan \alpha=2\sqrt{2},$$ then the value of $$\dfrac{\tan\alpha}{\dfrac{\sin^{3}\alpha}{\cos\alpha}+\sin\alpha.\cos\alpha}$$ is

If $$\cos A$$ $$=$$ 2 sin A, find the value of  $$cosec A$$.

The value of $$\sin^6 \theta+\cos^6 \theta+3 \sin^2\theta.\cos^2\theta$$ is

If $$x, y \in [0,2\pi]$$, then total number of ordered pairs $$(x, y)$$ satisfying the equation $$\sin x.\cos y=1$$ is equal to

The set of angles between $$0$$ & $$2\pi$$ satisfying the equation $$4 \cos^2\theta -2\sqrt 2 \cos\theta-1=0$$ is-