Q. 3 C

# For the principal

First of all we need to find the principal value for cosec–1(–2)

Let,

cosec–1–2 = y

cosec y = –2

–cosec y = 2

–cosec = 2

As we know cosec(–θ) = –cosecθ

–cosec = cosec

The range of principal value of cosec–1 is –{0} and

cosec = –2

Therefore, the principal value of cosec–1(–2) is .

Now, the question changes to

Sin–1[cos]

Cos(–θ) = cos(θ)

we can write the above expression as

Sin–1[cos]

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 .

Hence, the principal value of the given equation is .

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