Write each of the following in the simplest form:
Assume x = tanθ
= tan–1
= tan–1
= tan–1
= tan–1
= tan–1
Cos θ = 2 cos2
–1 and sinθ = 
⇒ 1 + cosθ = 2 cos2
= tan–1
= tan–1
= tan–1(cot
)
cot
= tan
= tan–1(tan
)
But θ = tan–1x.
∴ 
Therefore, the simplification of given equation is 
7