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If sin^(3)x cos3x+cos^(3)x sin 3x=3//8, ...

If `sin^(3)x cos3x+cos^(3)x sin 3x=3//8`, then the value of `sin 4x` is ___________

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The correct Answer is:
0.5
` 4 sin ^(3)x cos 3x + 4 cos ^(3)x sin 3x = (3)/(2)`
or `( 3sin x - sin3x ) cos 3x + ( 3 cosx +cos 3x) sin 3x = (3)/(2)`
or `3 [ sin x cos 3x + cos x sin 3x ] = (3)/(2)`
or `sin 4x = (1)/(2)`
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CENGAGE PUBLICATION-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Numerical Value Type )
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  2. If (tanx)/2=(tany)/3=(tanz)/5,x+y+z=pia n dtan^2x+tan^2y+tan^2z=(38)/K...

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  3. If sin^(3)x cos3x+cos^(3)x sin 3x=3//8, then the value of sin 4x is

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  4. The value of "cosec".(pi)/(18)-4 sin""(7pi)/(18) is

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  5. If tanx+tan2x+tan3x=tanxtan2xtan3x then value of |sin3x+cos3x| is

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  6. 16(costheta-cospi/8)(costheta-cos(3pi)/8)(costheta-cos(5pi)/8)(costhet...

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  7. If (tan(I n6)dottan(I n2)dot"tan"(I n3))/(tan(I n6)-tan(I n2)-"tan"(I ...

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  8. If cot(theta-alpha),3cottheta,"cot"(theta+alpha) are in A.P. and theta...

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  9. The value of (2 sinx)/(sin 3x)+(tanx)/(tan3x)

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  10. If cot^2Acot^2B=3, then the value of (2-cos2A)(2-cos2B) is

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  11. The value of f(x)=x^4+4x^3+2x^2-4x+7, when x=cot(11pi)/8 is

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  12. The value of sin^2 12^0+sin^2 21^0+sin^2 39^0+sin^2 48^0-sin^2 9^0-sin...

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  13. Given that f(ntheta)=(2sin2theta)/(cos2theta-cos4ntheta), and f(theta)...

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  14. Suppose sin^(3)x sin3x=sum(m=0)^(n) C(m) cos mx is an idedntity in x ...

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  15. If sec alpha is the average of sec(alpha - 2beta) and sec(alpha + 2bet...

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  16. If A, B and C are three values lying in [0, 2pi] for which tan theta =...

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  17. The value of [ ( sin ""(pi)/(9)) (4+ sec""(pi)/(9))]^(2) is .

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  18. ((sin 33^(@))/( sin 11^(@) sin 49^(@) sin 71^(@)))^(2) + (( cos 33^(@)...

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  19. If f( theta ) = sin ^(3)theta + sin ^(3)( theta + (2pi)/(3)) + sin ^(3...

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  20. The expression (1+sin22^@sin33^@sin35^@)/(cos^2 22^@+cos^2 33^@+cos^2 ...

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