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Question

If in ABC,a=5,b=4,A=π2+B, then C


A

is tan-112

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B

is tan-1940

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C

cannot be evaluated.

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D

is tan-119

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Solution

The correct option is B

is tan-1940


Explanation for the correct option.

Find the value of C:

Given,

a=5,b=4,A=π2+B.

We know that,

tanA-B2=a-ba+bcotC2tanπ22=5-45+4cotC21cotC2=19[tanπ4=1]tanC2=19[1cotθ=tanθ]

Again, we know that,

tanC=2tanC21-tan2C2=291-181=940

Therefore, C=tan-1940

Hence, the correct option B.


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