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Question

If cot-1(α)+cot-1(β)=cot-1(x), then x


A

α+β

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B

αβ

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C

(1+αβ)(α+β)

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D

(αβ1)(α+β)

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Solution

The correct option is D

(αβ1)(α+β)


Find the value of x:

Given, cot-1(α)+cot-1(β)=cot-1(x)

tan-11α+tan-11β=tan-11x

tan-11α+1β11α1β=tan-11x tan-1(a)+tan-1(b)=tan-1(a+b1ab)

tan-1β+ααβ1=tan-11x

α+βαβ1=1x

x=(αβ1)(α+β)

Hence, Option 'D is Correct.


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