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Question Number 73706 by Faradtimmy last updated on 15/Nov/19

If ((tan 3A)/(tan A)) = k, then ((sin 3A)/(sin A)) is equal to

Iftan3AtanA=k,thensin3AsinAisequalto

Answered by Tanmay chaudhury last updated on 15/Nov/19

tanA=t ((3t−t^3 )/(t(1−3t^2 )))=k→k−3kt^2 =3−t^2 t^2 (1−3k)=3−k tan^2 A=((3−k)/(1−3k)) cot^2 A=((1−3k)/(3−k))→cosec^2 A=((1−3k+3−k)/(3−k))=((4−4k)/(3−k)) sin^2 A=((3−k)/(4−4k)) ((sin3A)/(sinA)) =3−4sin^2 A =3−4(((3−k)/(4−4k)))=((12−12k−12+4k)/(4−4k))=((−8k)/(4−4k))=((2k)/(k−1))

tanA=t3t−t3t(1−3t2)=k→k−3kt2=3−t2t2(1−3k)=3−ktan2A=3−k1−3kcot2A=1−3k3−k→cosec2A=1−3k+3−k3−k=4−4k3−ksin2A=3−k4−4ksin3AsinA=3−4sin2A=3−4(3−k4−4k)=12−12k−12+4k4−4k=−8k4−4k=2kk−1

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