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Question

If cot2x=cot(xy).cot(xz) where x±π4, then cot2x=


A

12(coty+cotz)

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B

12(cotzcoty)

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C

12(cotz+1cot2)

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D

(coty+1coty)

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Solution

The correct option is A

12(coty+cotz)


cot2x=cot(xy).cot(xz)cot2x=(cotxcoty+1cotycotx)(cotxcotz+1cotzcotx)cot2x(cotycotx)(cotzcotx)=(cotxcoty+1)(cotxcotz+1)cot3x(coty+cotz)+cotx(coty+cotz)+1cot4x=0cotx(coty+cotz)(1+cot2x)+(1cot2x)(1+cot2x)=01+cot2x0cotx(coty+cotz)+(1cot2x)=0cot2x12cotx=12(coty+cotz)


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