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Question

The value of tantan-112-tan-113 is


A

56

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B

76

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C

16

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D

17

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Solution

The correct option is D

17


Explanation for the correct option

The given trigonometric expression: tantan-112-tan-113.

It is known that tan-1(A)-tan-1(B)=tan-1(A-B1+AB).

β‡’tantan-112-tan-113=tantan-112-131+1213β‡’tantan-112-tan-113=1Γ—3-1Γ—261+16β‡’tantan-112-tan-113=166+16β‡’tantan-112-tan-113=1676β‡’tantan-112-tan-113=17

Hence, option D is correct.


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