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Prove that tanpi/(16)+2tanpi/8+4=cotpi/(...

Prove that `tanpi/(16)+2tanpi/8+4=cotpi/(16)` .

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`cot theta-tan theta=(cos theta)/(sin theta)-(sin theta)/(cos theta)`
`=(cos^(2)theta-sin^(2)theta)/(sin thetacos theta)`
`=(2cos 2 theta)/(sin 2theta)`
`=2cot 2 theta`
`therefore cot theta-2cot 2 theta=tan theta `
Now, `tan"" (pi)/(16)+2tan ""(pi)/(8)+4`
`=(cot""(pi)/(16)-2cot""(pi)/(8))+2(cot""(pi)/(8)-2cot""(pi)/(4))+4`
`=cot""(pi)/(16)-4cot""(pi)/(4)+4=cot""(pi)/(16)`
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