Question

prove that 1-sin theta/1+sin theta=sec theta-tan theta​

Answer 1

LHS =

1+sinθ

1−sinθ

Multiply and divide by (1−sinθ)

=

1+sinθ

1−sinθ

×

1−sinθ

1−sinθ

=

cos

2

θ

(1−sinθ)

2

=(

cosθ

1−sinθ

)

2

=(secθ−tanθ)

2

=RHS

Hence proved