Question

If 8×cot theta=7 then evaluate

(1+cos theta)(1–cos theta)
——————————————
(1+sin theta)(1–sin theta)

Answer 1

64/49

Explanation:

8 cot θ = 7

cot θ = 7/8

tan θ = 8/7

[ (1 + cos θ) (1 – cos θ) ] / [ (1 + sin θ) (1 – sin θ) ]

Distribute:

(1 – cos² θ) / (1 – sin² θ)

Use Pythagorean identity:

sin² θ / cos² θ

Divide:

tan² θ

Substitute:

(8/7)²

64/49