Question

given cot theta is equals to 7/8 then evaluate 1. (1+sin(theta)(1-sin (theta)/1+cos (theta)(1-cos(theta) and 2. (1+sin (theta)/cos (theta)

Answer 1

1. using identity (a+b)(a-b)=a^2-b^2
(1-sin^2 theta)/(1-cos^2 theta)=cos^2 theta/sin^2 theta=cot^2 theta =(7/8)^2=49/64.

2. cot theta=7/8
sin theta = 8/sqrt(113)
cos theta=7/sqrt(113)
(1+sin theta)/cos theta = (sqrt(113)+8)/7