Write each of the following in the simplest form:

Put x = a cosθ

⇒ tan^{–1}

⇒ tan^{–1}

⇒ tan^{–1}

Rationalising it

tan^{–1}

⇒ tan^{–1}

⇒ tan^{–1}

⇒ tan^{–1}

Cos θ = 1 – 2 sin^{2} and sinθ =

⇒ 1 – cosθ = 2 sin^{2}

= tan^{–1}

= tan^{–1}

= tan^{–1}(tan)

=

But θ = cos^{–1}

∴ The given equation simplification to cos^{–1} .

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