Question

1 - cos theta + sin theta into 1 + cos theta + sin theta equals to 2 Sin Theta into 1 + sin theta​

Answer 1

(1-cos theta+sin theta)(1+cos theta + sin theta)

= (1+sin theta - cos theta)(1+sin theta + cos theta)........(1)

let a = 1+sin theta and b= cos theta

by using formula

(a-b)(a+b)= a^2 - b^2. in first equation

(1+sin theta)^2 - cos^2 theta

= 1+sin^2 theta + 2sin theta - cos^2theta

= 1-cos^2 theta + sin^2 theta +2sin theta

= sin^2 theta + sin^2 theta + 2sin theta

= 2 sin^2 theta + 2sin theta

= 2 sin theta (sin theta + 1)

hence proved