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Q.

Suppose α,β>0 and α+2β=π/2 , then tan⁡(α+β)−2tan⁡α−tan⁡β is equal to

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a

0

b

tan⁡β

c

cot⁡β

d

tan⁡α−cot⁡β

answer is A.

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Detailed Solution

tan⁡(α+β)=tan⁡(π/2−β)⇒ tan⁡α+tan⁡β1−tan⁡αtan⁡β=cot⁡β⇒ tan⁡α+tan⁡β=cot⁡β−tan⁡α⇒ 2tan⁡α+tan⁡β=cot⁡β=tan⁡(α+β)

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