Question

1+Sin/Cos + Cos/1+Sin = 2Sec

Answer 1

Step-by-step explanation:

Consider the left-hand side:

$\dfrac{1+\sin{\theta}}{\cos{\theta}} + \dfrac{\cos{\theta}}{1+\sin{\theta}}$

$\:\:\:\:= \dfrac{(1+\sin{\theta})^2 + \cos^2{\theta}}{\cos{\theta}(1+\sin{\theta})}$

$\:\:\:\:=\dfrac{1+2\sin{\theta}+\sin^2{\theta} + \cos^2{\theta}}{\cos{\theta}(1+\sin{\theta})}$

$\:\:\:\:=\dfrac{2+2\sin{\theta}}{\cos{\theta}(1+\sin{\theta})} =\dfrac{2(1+\sin{\theta})}{\cos{\theta}(1+\sin{\theta})}$

$\:\:\:\:= \dfrac{2}{\cos{\theta}} = 2\sec{\theta}$