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trignometry 1) solve sinx sin3x=1/2

trignometry
1) solve sinx sin3x=1/2

Grade:11

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
sinx(3sinx-4sin^3x)=1/2

2sin^2x(3-4sin^2x)=1

let sinx=t

2t^2(3-4t^2)=1

6t^2-8t^4-1=0

8t^4-6t^2+1=0

put t^2=y, we get

8y^2-6y+1=0

(2y-1)(4y-1)=0

y=1/2, 1/4

t^2=1/2, 1/4

t=1/root2, 1/2

=> sinx=1/root2 , 1/2

=> x=pi/4, pi/6

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

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