prove that : `tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = co – InterviewSolution

InterviewSolution

1.	prove that : `tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)`
Answer» We know that, `cot theta-tantheta=(1-tan^(2)theta)/(tan theta)=2((1-tan^(2)theta)/(2tantheta))=2cot 2 theta...(i)` LHS = `tan alpha + 2 tan 2 alpha + 4 tan 4 alpha + 8 cot 8 alpha` `=-(cotalpha - tan alpha - 2 tan 2 alpha - 4tan 4 alpha)+8cot 8 alpha + cot alpha` `=-(2cot 2alpha-2tan 2 alpha - 4tan 4 alpha)+8cot 8alpha + cotalpha" [from Eq. (i)]"` `=-(2(2cot 4 alpha)-4 tan 4 alpha)+8cot 8 alpha+cot alpha " [from Eq. (i)]"` `=-4(cot4 alpha-tan 4alpha)+8cot8alpha + cot alpha` `=-8cot 8 alpha +8cot 8 alpha + cot alpha " [from Eq. (i)]"` `=cot alpha = RHS`

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