Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 7 of Exercise 4.7
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7
Write each of the following in the simplest form:
Put x = cos θ
= sin–1(2tan–1
)
1 – cosθ = 2 sin2
and 1 + cos θ = 2 cos2
= sin–1(2tan–1
)
= sin–1(2tan–1
)
= sin–1(2tan–1(tan
))
= sin–1(
)
= sin–1(θ)
But θ = cos–1x
∴ The above expression becomes sin–1(cos–1x)
