Answer :

We need to find the value of 2 tan-1 |cosec(tan-1 x) – tan(cot-1 x)|.

So, take

2 tan-1 |cosec(tan-1 x) – tan(cot-1 x)|

Using property of inverse trigonometry,

Now, let y = tan-1 x

So, tan y = x

Substituting the value of tan-1 x and x in the equation,


Since, we know the trigonometric identity,

1 – cos 2y = 2 sin2 y

Also, sin 2y = 2 sin y cos y

We get,



2 tan-1 |cosec(tan-1 x) – tan(cot-1 x)| = y

Put y = tan-1 x as let above.

2 tan-1 |cosec(tan-1 x) – tan(cot-1 x)| = tan-1 x

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