Question

Proove that
1/1-sin theta + 1/1+cos theta = 2×sec square theta ​

Answer 1

Explanation:

We are to show that 1/1-sin theta + 1/1+cos theta = 2×sec square theta ​

Starting from the left hand side of the expression:

1/1-sin theta + 1/1+cos theta

Find the LCM

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