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Question

Prove that tan50°-tan40°=2tan10°


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Solution

To Prove

tan50°-tan40°=2tan10°

Use formula:

tan(a+b)=(tana+tanb)(1-tanatanb)

Consider

tan50=tan(40+10)tan50=(tan40+tan10)(1-tan40tan10)Crossmultiplytan50(1-tan40tan10)=tan40+tan10tan50tan50tan40tan10=tan40+tan10tan50=tan(90-40)=cot40andcot40tan40=1tan50tan10=tan40+tan10tan50tan40=tan10+tan10tan50tan40=2tan10

Hence, proved.


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