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)