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Solve sin^2x +1/4sin^2 3x=sinxsin^2 3x...

Solve `sin^2x +1/4sin^2 3x=sinxsin^2 3x`

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`sin^2x+1/4sin^2 2x=sinxsin^2 3x`
`sin^2x-sinxsin^2 3x+1/4sin^2 3x=0`
`(sinx-1/2sin^2 3x)^2-1/4sin^4 3x+1/4sin^2 3x=0`
`(sinx-1/2sin^2 3x)^2+1/4sin^2 3x[-sin^2 3x+1]=0`
`(sinx-1/2sin^2 3x)^2+1/4sin^2 3xcos^2 3x=0`
`(sinx-1/2sin^2 3x)^2+1/4*(sin^2 6x)/4=0`
`(sinx-1/2sin^2 3x)^2+1/16sin^2 6x=0`
`(sinx-1/2sin^2 3x)^2+(1/4sin6x)^2=0`
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CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Solve the equation sin^4x+cos^4x-2sin^2x+(3sin^2 2x)/4=0

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  2. sin^2(A/2)+sin^2(B/2)-sin^2(C/2)=1-2cos(A/2)cos(B/2)sin(C/2)

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  3. Solve sin^2x +1/4sin^2 3x=sinxsin^2 3x

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  4. In any triangle ABC, prove that sin^3Acos(B-C)+sin^3Bcos(C-A)+sin^3Cco...

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  5. Find the smallest positive root of the equation sqrt(sin(1-x))=sqrt(co...

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  6. cot16^0cot44^0+cot44^0cot76^0-cot76^0cot16^0= (a)1(b) 2 (c)3 (d) ...

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  7. Solve the equation tan^4x+tan^4y+2cot^2xcot^2y=3+sin^2(x+y) for the va...

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  8. The value of (2sinx)/(sin3x)+(tanx)/(tan3x) is.

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  9. Prove that the equation 2 sin x=|x|+a has no solution for a in ((3sqrt...

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  10. Prove that tanpi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

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  11. Solve the equation 2sinx+cosy=2 for the value of xa n dydot

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  12. Find the value of cos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)

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  13. Prove that sintheta+sin3theta+sin5theta+.....+sin(2n-1)theta=(sin^2nth...

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  14. Prove that (cos3x)/(sin2xsin4x)+(cos5x)/(sin4xsin6x)+(cos7x)/(sin6xsi...

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  15. Prove that 2sin2^0+4sin4^0+6"sin"6^0+.......+180sin180^0=90cot1^0dot

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  16. If A+B+C=180 , prove that cos^2A+cos^2B+cos^2C=1-2cosAcosBcosCdot

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  17. Prove that in triangle A B C ,cos^2A+cos^2B-cos^2C=1-2sinAsinBcosCdot

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  18. In triangle ABC, prove that sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sin Asi...

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  19. Prove that sum(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2, wherengeq3 is an int...

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  20. If (tan(ln6)dottan(ln2)dot"tan"(ln3))/(tan(ln6)-tan(ln2)-"tan"(ln3))=k...

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