Question

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

Answer 1

Explanation:

Consider the left-hand side:

`(1+sin(\theta))/(cos(\theta)) + (cos(\theta))/(1+sin(\theta))`

`\:\:\:\:= \frac{(1+sin(\theta))^2 + \cos^2{\theta}}{cos(\theta)(1+sin(\theta))}`

`\:\:\:\:=\frac{1+2sin(\theta)+\sin^2{\theta} + \cos^2{\theta}}{cos(\theta)(1+sin(\theta))}`

`\:\:\:\:=(2+2sin(\theta))/(cos(\theta)(1+sin(\theta))) =(2(1+sin(\theta)))/(cos(\theta)(1+sin(\theta)))`

`\:\:\:\:= (2)/(cos(\theta)) = 2\sec{\theta}`