Question

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

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

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.