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 sin2
and sinθ = 
⇒ 1 – cosθ = 2 sin2
= tan–1
= tan–1
= tan–1(tan
)
= 
But θ = cos–1
∴ The given equation simplification to cos–1
.
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