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Question

Solve for x: 2tan1(sinx)=tan1(2secx)

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Solution

2tan1(sinx)=tan1(2secx)
We know, 2tan1x=tan1(2x1x2)
So, 2tan1(sinx)=tan1(2sinx1sin2x)
According to the question,
tan1(2sinx1sin2x)=tan1(2secx)

2sinx1sin2x=2cosx

sinxcos2x=1cosx

sinx=cosx

sinxcosx=1

tanx=1

x=tan1(1)

x=π4

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