Given tan A \(\frac { 4 }{ 3 } \) find the other trigonometric ratios of the angle A.

Prove that \(\frac { sin\theta -cos\theta +1 }{ sin\theta +cos\theta -1 } =\frac { 1 }{ sec\theta -tan\theta } \) using the identity sec²θ= 1+ tan²θ.

Prove that sec A (1 - sin A) (sec A + tan A) = 1.

In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.