Question

Prove that `sqrt((1+sintheta)/(1-sintheta))+sqrt((1-sintheta)/(1+sintheta))=2sectheta`

Answer 1

We have
`LHS= sqrt((1+ sin theta)/(1- sin theta)) + sqrt((1- sin theta)/(1+ sin theta)) `
` =(sqrt(1+ sin theta))/(sqrt(1- sin theta))+ (sqrt(1- sin theta))/(sqrt(1+ sin theta))= (1+ sin theta +1 - sin theta)/(sqrt((1- sin theta)(1+ sin theta)))`
`= (2)/(sqrt((1-sin^(2) theta))) = (2)/(sqrt(cos^(2)theta))= (2)/(cos theta) = 2 sec theta = RHS. `
` therefore LHS = RHS. `