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If tan3A=3tan A +k tan^3A/1-3tan^2A,then k is equal to 
Asked by azizrajil03 | 30 Jan, 2019, 07:13: AM
answered-by-expert Expert Answer
we have begin mathsize 12px style tan open parentheses A plus B close parentheses space equals space fraction numerator tan A plus tan B over denominator 1 minus tan A tan B end fraction end style
hence begin mathsize 12px style tan left parenthesis 3 A right parenthesis space equals space tan left parenthesis A plus 2 A right parenthesis space equals space fraction numerator tan A plus tan 2 A over denominator 1 minus tan A space tan 2 A end fraction space equals space fraction numerator tan A space plus begin display style fraction numerator 2 tan A over denominator 1 minus tan squared A end fraction end style over denominator 1 minus tan A begin display style fraction numerator 2 tan A over denominator 1 minus tan squared A end fraction end style end fraction space equals space fraction numerator 3 tan A minus tan cubed A over denominator 1 minus 3 tan squared A end fraction end style  ....................(1)
By comparing the given trignometric expression in question with eqn.(1), we get k = -1
Answered by Thiyagarajan K | 30 Jan, 2019, 11:04: AM

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