Question

★ PROVE THE IDENTITY ★

1-sinΦ/1+sinΦ = (secΦ -tan Φ) ^2

★ CONTENT QUALITY SUPPORT REQUIRED ★

Answer 1

L.H.S
1-sin∅/1+sin∅
♪ Multiplying And Dividing By 1-sin∅ ♪
= 1-sin∅/1+sin∅×1-sin∅/1-sin∅

= (1-sin∅)²/1-sin²∅
= (1-sin∅)²/cos²∅
= (1-sin∅/cos∅)²
= (1/cos∅-sin∅/cos∅)²
= (sec∅-tan∅)²
= R.H.S
hence L.H.S = R.H.S

Answer 2

Hey there!


LHS = 1-sinΦ/ 1+sinΦ

= 1-sinΦ/ 1+sinΦ * 1-sinΦ /1-sinΦ

=( 1-sinΦ)^2 / 1-sin^2 Φ

= (1- sin^2Φ )/ cos^2Φ

=( 1-sinΦ/cosΦ)^2

= [ 1/cosΦ -sinΦ/cosΦ ] ^ 2

= (secΦ -tanΦ)^2 = RHS


Hence proved!


#hope it helps!