Trigonometric F...

$$(\text{cosec} \theta - \sin \theta)(\sec \theta - \cos \theta)(\tan \theta + \cot \theta)$$ simplifies to

The value of $$ \cos^4\theta-\sin^4 \theta+2 \sin^2 \theta$$ is equal to 

Which of the following is/are FALSE   $$\forall \theta \in R$$?

If $$\tan\theta=\dfrac{3}{4}$$ and $$0< \theta, < 90^0,$$ then the value of $$\sin\theta \cos \theta$$ is

$$\dfrac{3-4 \sin^2 \theta}{\cos^2 \theta}$$ is equal to

$$(1-\sin^2 \theta)(1+\tan^2 \theta)$$ is equal to

$$\dfrac{\tan^{2}\theta}{(1+\sec \theta)^{2}}$$ is equal to

$$\sec^2 \theta +\text{cosec}^2 \theta$$ is equal to

The expression $$\sin^6 \theta+\sin^4 \theta \cos^2 \theta - \sin^2 \theta \cos^4 \theta - \cos^6 \theta$$ can be reduced to

$$\dfrac{\cos A}{1-\tan A} + \dfrac{\sin A}{1 - \cot A}$$is equal to