Question

Sec theta - tan theta / sec theta + tan theta = cos^2 theta / (1 + sin theta ) ^2​

Answer 1

sec∅ - tan∅

sec∅ + tan∅

1 - sin∅

=cos∅ cos∅

1 + sin∅

cos∅ cos∅

1-sin∅

= cos∅

1+sin∅

cos∅

=1- sin∅

1+sin∅

multiplying both with (1+sin∅)

= 1-sin∅ × 1+sin∅

1+sin∅ 1+ sin∅

= 1²- sin²∅

(1+sin∅)²

= cos²∅

(1+sin∅)²

= R.H.S