Question

prove the following
root 1-sin theta/ 1+sin theta = sec theta- tan theta
​

Answer 1

Step-by-step explanation:

what you need to do is to rationalize

the LHS BY

dividing and multipying by 1-sin theta/1-sin theta

then the root will open and you will get

1-sin theta / costheta

as 1- sin^2theta is cos^2theta

now break them into two

1/costheta - sintheta/costheta

you get sec theta - tan theta

Answer 2

Step-by-step explanation:

Take L.H.S

root 1-sin theta /1+sin theta

root (1-sin theta)^2 /(1+sin theta)(1-sin theta)

root (1-sin theta)^2/1- sin^2 theta

root(1-sin theta)^2/ cos^2 theta

Cancelling the square roots

1 - sin theta / cos theta

1/cos theta - sin theta / cos theta

sec theta - tan theta = R.H.S

Hence proved