Question

sec theta - tan theta =√3 -2 show that 1-sintheta/1+sin theta = 7-4√3

Answer 1

SecΘ - TanΘ = √3 - 2
=> (1 / CosΘ) - (SinΘ / CosΘ) = √3 - 2
=> (1 - SinΘ) / CosΘ = √3 - 2
Squaring both sides,
=> {(1 - SinΘ) / CosΘ}² = ( √3 - 2 )²
=> (1 - SinΘ)(1 - SinΘ) / Cos²Θ = 3 - 4√3 + 4
=> (1 - SinΘ)(1 - SinΘ) / (1 - Sin²Θ) = 7 - 4√3
=> (1 - SinΘ)(1 - SinΘ) / (1 - SinΘ)(1 + SinΘ) = 7 - 4√3
=> (1 - SinΘ) / (1 + SinΘ) = 7 - 4√3

Hence proved.

Hope this helps.