Question

If sec - tan = root 3 - 2 show that 1- sin / 1+sin= 7- 4root 3

Answer 1

???i dont know,.............

Answer 2

sec-tan whole sq = root 3-2 whole sq

sec^2+tan^2-2sectan = 3+4-4root3

1/cos^2+sin^2/cos^2+2sin/cos^2 = 7-4 root3

simplifying lhs

sin^2-2sin+1/cos^2

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

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

= 1(1-sin)-sin(1-sin)/(1+sin)(1-sin)

= (1-sin)(1-sin)/(1+sin)(1-sin)

= 1-sin/1+sin

therefore, 1-sin/1+sin = 7-4root3