Question

Show that :

(sec∅ - tan∅)² = 1-sin∅/1+sin∅​

Answer 1

Question :-

Show that :

(sec∅ - tan∅)² = 1-sin∅/1+sin∅

Solution :-

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

= [1-sin∅/cos∅]² = (1 - sin∅)²/cos²∅

= (1-sin∅)²/1-sin²∅ = (1-sin∅)(1-sin∅)/(1-sin∅)(1+sin∅)

= 1-sin∅/1+ sin∅

Answer 2

LHS

(sec@ - tan@)^2

(1 - sin@)^2/cos^2@

using formula

cos^2@ = /(1 + sin@)(1 - sin@)

(1 - sin@)^2/(1 + sin@)(1 - sin@)

(1 - sin@ )/(1 + sin@)

Hence LHS = RHS

proved