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Question

Prove that: cot π8=2+1

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Solution

π8=2212°Let A=2212°Using the identity cot2A=cot2A-12cotA, we getcot45°=cot22212°-12cot2212° 1=cot22212°-12cot2212° cot45°=12cot2212°-cot22212°+1=0

cot22212-2cot2212-1=0cot22212-2cot2212+1-2=0cot2212-12=2cot2212-1=2cot2212=2+1

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