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Question

Prove that cot(π42cot13)=7.

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Solution

cot(π42cot13)=7let2cot13=θcot13=θ2cotθ2=3tanθ2=13cot(π4θ)=7cotπ4cotθ+1cotθcotπ4=7cotθ+1cotθ1=71+tanθ1tanθ=1+2tanθ21tan2θ212tanθ21tan2θ2Puttanθ2=131+231191231191+23×98123×981+341347414=7cot(π42cot13)=7proved

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