Question

Which of the following expressions can be used to complete the equation below Secx / 1+cot^2x=

Tan x
Tan^2 x
Tan x cos x
Tan x sin x

Answer 1

Answer: D) Tan x sin x

Explanation:

`(sec)/(1+cot^2)\\\\\\=(1)/(cos)\cdot (1)/(1+cot^2)\\\\\\=(1)/(cos)\cdot (1)/(1+((cos)/(sin))^2)\\\\\\=(1)/(cos)\cdot (1)/(((sin^2)/(sin^2))+((cos^2)/(sin^2)))\\\\\\=(1)/(cos)\cdot (sin^2)/(sin^2+cos^2)\\\\\\=(1)/(cos)\cdot (sin^2)/(1)\\\\\\=(sin\cdot sin)/(cos\cdot 1)\\\\\\=\boxed{tan\cdot sin}`