Question

prove that cos theta by 1 - sin theta equals to 1 + sin theta by cos theta​

Answer 1

The given equation is:

\frac{cos\theta}{1+sin{\theta}}=\frac{1-sin{\theta}}{cos{\theta}}

Taking the LHS of the above equation, we have

\frac{cos\theta}{1+sin{\theta}}

=\frac{cos\theta}{1+sin{\theta}}{\times}\frac{1-sin\theta}{1-sin{\theta}}

=\frac{cos\theta(1-sin\theta)}{1-sin^2{\theta}}

=\frac{cos\theta(1-sin\theta)}{cos^2{\theta}}

=\frac{1-sin{\theta}}{cos{\theta}}

=RHS

Hence proved.