Question

If θ is an acute angle such that tan²θ = 8/7, then the value of
(1+sin????)(1-sin????)/(1+cos????)(1-cos????) is
A. 7/8
B. 8/7
C. 7/4
D. 64/49

Answer 1

A. 7/8

Step-by-step explanation:

Given: tan²θ = 8/7

Find: (1+sinθ )(1-sinθ) / (1+cosθ)(1-cosθ)

Solution:

(1+sinθ )(1-sinθ) / (1+cosθ)(1-cosθ)

= 1 - Sin²θ / 1- Cos²θ

= Cos²θ / Sin²θ

= Cot²θ

= 1/tan²θ

= 1/ (8/7)

= 7/8

Option A is the answer.