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Question

Evaluate tan-13x-x31-3x2-tan-12x1-x2:


A

0

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B

1

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C

tan-1x

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D

tan-12x

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Solution

The correct option is C

tan-1x


Explanation for correct option

Evaluating the given trigonometric expression:

Given, the expression is: tan-13x-x31-3x2-tan-12x1-x2

We know that:

tan-1a-tan-1b=tan-1a-b1+ab...(i)

Here,

a=3x-x31-3x2 and b=2x1-x2

Now, applying a and b in equation (i):

tan-13x-x31-3x2-tan-12x1-x2=tan-13x-x31-3x2-2x1-x21+3x-x31-3x2×2x1-x2

Cross-multiplying further,

=tan-13x-x31-x2-2x1-3x21-3x21-x2+2x3x-x3

=tan-13x-3x3-x3+x5-2x+6x31-x2-3x2+3x4+6x2-2x4=tan-1x5+2x3+xx4+2x2+1

=tan-1xx4+2x2+1x4+2x2+1

=tan-1x

Therefore, the value is tan-1x.

Hence, the correct answer is Option (C).


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