Q. 33.7( 3 Votes )

# Choose the correc

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, Put,    Since, we know the trigonometric identity,

1 – cos 2y = 2 sin2 y Also, sin 2y = 2 sin y cos y We get,  Since, Then,  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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