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Question

sec(cosec-1x) is equal to


A

cosec(sec-1x)

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B

cotx

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C

π

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D

None of these

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Solution

The correct option is A

cosec(sec-1x)


Explanation for the correct option:

Finding trigonometric relations to solve the given equation:

Assume the value of cosec-1x=A

Then, the value of cosecA=x and hence sinA=1x.

Using the trigonometric identity to get the cosine value.

sin2A+cos2A=1cosA=1-sin2AcosA=1-1x2cosA=x2-1x

So, using the obtained value to find the secant value.

secA=xx2-1[cosx=1secx]seccosec-1x=xx2-1[cosec-1x=A,assumed]

Again, assume sec-1x=B

Then, the value of secB=x

So, cosB=1x

Determining the sine value for the assumption.

Use the trigonometric identity to get the sine value.

sin2B+cos2B=1sinB=1-cos2B=1-1x2=x2-1x

So, using the obtained value to find the cosecant value.

cosecB=xx2-1cosecsec-1x=xx2-1

So, seccosec-1x=cosecsec-1x

Hence, option (A) is the correct answer.


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