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 cos^{2} –1 and sinθ =

⇒ 1 + cosθ = 2 cos^{2}

= tan^{–1}

= tan^{–1}

= tan^{–1}(cot)

cot = tan

= tan^{–1}(tan)

But θ = tan^{–1}x.

∴

Therefore, the simplification of given equation is

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