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Question Number 43346 by peter frank last updated on 10/Sep/18
sinx−sin5x=sin3xfindtheanglethatsatisfiedtheequestion
Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18
sinx=sin5x+sin3xsinx=2sin4x.cosxsinx=2(2sin2xcos2x)cosxsinx=4(2sinxcosx)cos2xcosxsinx−8sinxcos2x.cos2x=0sinx(1−8cos2x.cos2x)=0onesolutionsinx=0=sinnΠx=nΠ1−8cos2x.cos2x=04(2cos2x)cos2x=14(1+cos2x)cos2x=1a=cos2x4(1+a)a=14a+4a2−1=04a2+4a−1=0a=−4±16−4×4×(−1)2×4a=−4±422×4a=42−42×4and−42−42×4a=2−12and−(2+1)2←thisnotfeasiblesoln1⩾cos2x⩾−1socos2xcannotbe−(2+1)2cos2x=2−12≈cos78ox≈39orechecksinx−sin5x=sin3xLHSsin39o−sin(195o)≈0.89RHSsin(117o)≈0.89
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