Question

2tan inverse (sin x)=tan inverse (2 sec x), find x​

Answer 1

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=