2tan inverse (sin x)=tan inverse (2 sec x), find x
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Answer:
2tan−1(sinx)=tan−1(2secx)
We know, 2tan−1x=tan−1(1−x22x)
So, 2tan−1(sinx)=tan−1(1−sin2x2sinx)
According to the question,
tan−1(1−sin2x2sinx)=tan−1(2secx)
⇒ 1−sin2x2sinx=cosx2
⇒ cos2xsinx=cosx1
⇒ sinx=cosx
⇒ cosxsinx=1
⇒ tanx=1
⇒ x=tan−1(1)
∴ x=
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