Question

tan inverse((sin x +cos x) ÷(cos x - sin x)

Answer 1

step 1: dividing Cos x in both nominator and denominator.
step 2: then the equation comes as
tan inverse((1+tan x)÷(1-tan x))
=tan inverse((tan π/4+ tan x)÷(1-tanx.tanπ/4))
= tan inverse(tan (π/4 + x))
=π/4 +x

Answer 2

Given:

tan inverse((sin x +cos x) ÷(cos x - sin x).

To find:

The value of the given expression.

Solution:

1) First we will divide all terms under tan by cos x.

2) we get the term as

• tan⁻¹((sin x +cos x)/ cos x ÷(cos x - sin x)/cos x)

• tan⁻¹((1 + tan x) ÷(1 - tan x))

• tan⁻¹((tanπ/4 + tan x) ÷(tanπ/4 - tan x))

• tan⁻¹(tan(π/4 + x)

• π/4 + x

tan inverse((sin x +cos x) ÷(cos x - sin x) is π/4 + x