Question

Solve for x : 2tan−1(sinx)=tan−1(2secx),0

Answer 1

We have, 2 tan−1(sinx) = tan−1(2 sec x)

Now, using 2tan−1(x) = tan−1( 2 x/1-x^2)

So, tan−1(2 sin (x)/1-sin^2 (x) ) = tan−1( 2 sec (x) )

or 2 sin (x)/cos^2 (x) = 2/cos (x)

{ Using sec x = 1/cos (x) and 1 - sin^2 (x) = cos^2 (x) }

So, Sin (x)/Cos (x) = 1

or tan (x) = 1

or x = π/4

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