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Question

If in a ABC, A=tan-12 and B=tan-13, then angle C is


A

π2

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B

π3

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C

π4

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D

None of these.

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Solution

The correct option is C

π4


Explanation for the correct option.

Find the angle C:

Given,

A=tan-12 and B=tan-13.

In a triangle A+B+C=π.

A+B+C=πtan-12+tan-13+C=πtan-12+31-2×3+C=π[tan-1x+tan-1y=π-tan-1x+y1-xy,xy>1]π-tan-15-5+C=ππ-tan-1-1+C=ππ-π4+C=π[tan-1(-1)=-π4]C=π4

Hence, the correct option is C.


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