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Solve the equation sin^3x.cos3x+cos^3x.s...

Solve the equation `sin^3x.cos3x+cos^3x.sin3x+3/8=0`

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`sin^3xcos3x+cos^3xsin3x +3/8 = 0`
`=>sin^3x(4cos^3x - 3cosx)+cos^3x(3sinx-4sin^3x)+3/8 = 0`
`=>4sin^3xcos^3x - 3cosxsin^3x+3sinxcos^3x - 4sin^3xcos^3x +3/8 = 0`
`=>3sinxcosx(cos^2x-sin^2x) = -3/8`
`=>8sinxcosx(cos2x) = -1`
`=>4sin2xcos2x = -1~
`=>2sin4x = -1`
=>sin4x = -1/2`
...
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CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
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  2. If cos(x+pi/3)+cos x=a has real solutions, then (a) number of inte...

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  3. Solve the equation sin^3x.cos3x+cos^3x.sin3x+3/8=0

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  7. For the equation 1-2x-x^2=tan^2(x+y)+cot^2(x+y) (a)exactly one valu...

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  9. For the smallest positive values of xa n dy , the equation 2(sinx+sin...

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  10. The minimum vertical distance between the graphs of y=2+sinx and y=cos...

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  11. Solve sinx+sinsqrt(((pi/8-cos2x)^2+sin^2 2x))=0

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  12. Suppose sin^3xsin3x=sum(m=0)^n Cmcosm x is an identity in x , where ...

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  13. Solve tan(pi/2costheta)=cot(pi/2sintheta)

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  14. The value of sum(r=0)^(10)cos^3((rpi)/3) is equal to (a)1/4 (b) 1/...

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  15. Solve the equation sin^4x+cos^4x-2sin^2x+(3sin^2 2x)/4=0

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  16. If A+B+C =pishow that cos^2 (A/2)-cos^2 (B/2)-cos^2 (C/2)=-2sin(A/2)co...

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

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

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

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

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