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Evaluate each of the following:
For finding the solution we first of need to find the principal value of
Sin–1
Let,
Sin–1 =y
⇒ sin y =
⇒ sin
The range of principal value of sin–1 is and sin
Therefore, the principal value of Sin–1 is
∴ The above equation changes to cot–1(2cos)
Now we need to find the value of 2cos
∴ cos
⇒ 2cos = 1 x
⇒ 2cos = 1
Now the equation simplification to cot–1(1)
Let cot–1(1) = y
⇒ cot y = 1
= cot = 1
The range of principal value of cot–1is (0, π)
and cot = 1
∴ The principal value of cot–1(2cos(Sin–1)) is