Question

Prove that 1/1-sin theta + 1/1+ sin theta = 2 sec^2 theta

Answer 1

Step-by-step explanation:

1+sin theta +1- sin theta/(1-sintheta )(1+sintheta)

2/1-sin^2theta

2×1/cos^2theta

2sec^2theta

Answer 2

Step-by-step explanation:

LHS = ( 1/1-sinθ) + (1/1+sinθ)

= [1+sinθ+1-sinθ]/(1-sin²θ)

= 2/cos²θ ( since , 1/cosθ =Secθ)

= 2sec²θ

Therefore LHS = RHS