Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

sec(cosec-1x) is equal to

1) cosec(sec-1x)

2) cot x

3) π

4) None of these

Answer: (1) cosec(sec-1x)

Solution:

Let cosec-1x = A

cosec A = x

sin A = 1/x

Using the identity sin2A + cos2A = 1,

cos A = [√(x2 – 1)]/x

sec A = x/√(x2 – 1)

Thus, sec(cosec-1x) = sec A = x/√(x2 – 1)

Now let us take sec-1x = B

sec B = x

cos B = 1/x

Therefore, sin B = [√(x2 – 1)]/x

cosec B = x/√(x2 – 1)

cosec(sec-1x) = cosec B = x/√(x2 – 1)

Hence, sec(cosec-1x) = cosec(sec-1x)

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