Question

Prove that (sec theta-tan theta)² =1-sin theta divided by 1+sin theta​

Answer 1

Answer:

(sec theta-tan theta)² =1-sin theta/1+sin theta

LHS,

(sec theta-tan theta)²

= (1/cos theta- sin theta/ cos theta)²

= (1 - sin theta/ cos theta)²

= {(1 - sin theta)(1 - sin theta)}/ cos² theta

= {(1 - sin theta)(1 - sin theta)}/ 1 - sin² theta

= {(1 - sin theta)(1 - sin theta)}/ 1² - sin² theta

= {(1 - sin theta)(1 - sin theta)}/ (1 - sin theta) (1 + sin theta)

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

= RHS