Question

1+sin theta - cos theta/1+ sin theta + cos theta = 1 - cos theta 1+ cos theta

Answer 1

Answer:

Answer to the question,

L.H.S

(1+sinФ-cosФ/1+sinФ+cosФ)²

=(1+sinФ-cosФ)²/(1+sinФ+cosФ)²

=(1+sinФ)²-2(1+sinФ)cosФ+cos²Ф/(1+sinФ)²+2(1+sinФ)cosФ+cos²Ф

=1+2sinФ+sin²Ф-(2+2sinФ)cosФ+cos²Ф/1+ 2sinФ+sin²Ф+(2+2sinФ)cosФ+cos²Ф

=1+2sinФ+sin²Ф+cos²Ф-2cosФ-2sinФcos/1+2sinФ+sin²Ф+cos²Ф+2cosФ+2sinФcosФ

=1+2sinФ+1-2cosФ-2sinФcosФ/1+2sinФ+1+2cosФ+2sinФcosФ

=2+2sinФ-2cosФ-2sinФcosФ/2+2sinФ+2cosФ+2sinФcosФ

=2(1+sinФ)-2cosФ(1+sinФ)/2(1+sinФ)+2cosФ(1+sinФ)

=2(1+sinФ)(1-cosФ)/2(1+sinФ)(1+cosФ)

=1-cosФ/1+cosФ

= R.HS