Introduction to...

Which of the following pair is a correct trignometric inter-relationship?

If $$\sin { 7\theta  } =\cos { 2\theta  } $$ for acute angles $$7\theta$$ and $$2\theta$$, then $$\theta =$$

The value of $$\tan 26^{\circ}\tan 64^{\circ}$$ is

The value of $$\sec 29^{\circ} - \text{cosec } 61^{\circ}$$

If $$\tan \theta + \cot \theta = 2$$, then the value of $$\tan^{2}\theta + \cot^{2}\theta$$ is  ____________.

If $$3x \csc 36^{\circ} = \sec 54^{\circ}$$, then the value of $$x$$ is

If $$4\tan \theta = 3$$, then $$\dfrac {5\sin \theta + 3\cos \theta}{5\sin \theta - 3\cos \theta} = $$

If $$ cos\, 25^0 +sin \, 25^0=k$$, then $$cos\, 20^0$$ is equal to 

Choose the correct answers from the alternatives given.
If $$0^{\circ} \leq  A \leq  90^{\circ}$$. the simplified form of the given expression $$\sin A  \cos A (\tan A- \cot A)$$ is

Evaluate: $$\displaystyle\frac{-\tan\theta \cot(90^o-\theta)+\sec\theta cosec(90^o-\theta)+\sin^235^o+\sin^255^o}{\tan 10^o\tan 20^o\tan 30^o \tan 70^o \tan 80^o}$$.