Question

prove that step by step

Answer 1

$LHS=\sqrt{\frac{1-sin{\theta}}{1+sin{\theta}} } \\=\sqrt{\frac{(1-sin{\theta})(1+sin{\theta})}{(1+sin{\theta})^2} }\\=\frac{\sqrt{(1-sin^2{\theta})}}{1+sin{\theta}} \\ =\frac{cos{\theta}}{1+sin{\theta}} \\ =\frac{cos{\theta}.(1+sin{\theta})}{1-sin^2{\theta}} \\ =\frac{(1+sin{\theta})}{cos{\theta}} \\ =sec{\theta}+tan{\theta}=RHS$