Question

prove that: cos theta divided by 1 + sin theta equals to 1 minus sin theta divided by cos theta​

Answer 1

To prove that:

cosθ / (1+sinθ) = (1 − sinθ) / cos θ

LHS =   cosθ / (1+sinθ) ..................................(a)

multiplying and dividing (a) by (1 - sinθ)

= [cosθ / (1+sinθ)] x [ (1 - sinθ) / (1 - sinθ) ]

= [cosθ (1 - sinθ) ] / (1 - sin²θ)

= [cosθ (1 - sinθ) ] / (cos²θ)

= (1 - sinθ) / cosθ

=RHS

Hence proved.