Question

show that: [sec theta-tan theta]sq = 1-sin theta/1+sin theta

Answer 1

(sec∅-tan∅)²=1-sin∅/1+sin∅

(sec∅-tan∅)²=1-sin∅/1+sin∅sec∅-tan∅= √[1-sin∅/1+sin∅]

$R.H.S.:- √(1-sin∅/1+sin∅)$

$=√[(1-sin∅)(1+sin∅)]/[(1+sin∅)(1+sin∅)]$

$=√[(1-sin²∅)]/[(1+sin∅)(1+sin∅)]$

$=√[cos²∅]/[(1+sin²∅)]$

$= (cos∅)/(1+sin∅)$

$=sec∅-tan∅$