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Find the value of the expression 3[sin...

Find the value of the expression
`3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(3pi+alpha)]-2[sin^(6)((pi)/(2)+alpha)+sin^(6)(5pi-alpha)]`.

Text Solution

AI Generated Solution

To find the value of the expression \[ 3\left[\sin^4\left(\frac{3\pi}{2}-\alpha\right)+\sin^4(3\pi+\alpha)\right]-2\left[\sin^6\left(\frac{\pi}{2}+\alpha\right)+\sin^6(5\pi-\alpha)\right], \] we will simplify each term step by step. ...
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find the value of the expression 3[sin^(4)(3(pi)/(2)-alpha)+sin^(4)(3 pi+alpha)]-2[sin^(6)((pi)/(2)+alpha)+sin^(6)(5 pi-alpha)]

The expression 3[sin^(4)((3)/(2)pi-alpha)+sin^(4)(3 pi+alpha)]-2[sin^(6)((1)/(2)pi+alpha)+sin^(6)(5 pi-alpha)] is equal to

Knowledge Check

  • The expression 3{sin^(4)((3pi)/(2)-alpha)+sin^(4)(3pi-alpha)} -12{sin^(6)((pi)/(2)+alpha)+sin^(6)(5pi-alpha)} is equal to

    A
    0
    B
    1
    C
    3
    D
    `sin4 alpha +cos 6 alpha`

  • The value of 3[sin^(4) ((3 pi)/(2)-alpha)+sin^(4) (3 pi +alpha)]-2[sin^(6) ((pi)/(2)+alpha)+sin^(6) (5 pi-alpha)] is

    A
    0
    B
    1
    C
    3
    D
    `sin 4 alpha + sin 6 alpha`

  • The expression 3[sin^4((3pi)/2+alpha)+sin^4((3pi)+alpha)] is -2 [sin^6(pi/2+alpha)+sin^6(5pi-alpha)] equal to

    A
    0
    B
    1
    C
    3
    D
    `sin 4alpha+cos 6alpha`

    • Similar Questions

    Explore conceptually related problems

    Find the value of the expression 3{sin^(4)((3 pi)/(2)-theta)+sin^(4)(3 pi+theta)}-2{sin^(6)((pi)/(2)+theta)+sin^(6)(5 pi-theta)}

    sin ^ (3) ((2 pi) / (3) + alpha) = (1) / (4) (3sin ((2 pi) / (3) + alpha) -sin (2 pi + 3 alpha)

    The expression 3[ sin^(4) ((3)/(2) pi - alpha) + sin^(4) (3 pi + alpha ) ] - 2 [ sin^(6) (( 1)/( 2) pi + alpha) + sin^(6) ( 5 pi - alpha)] is equal to

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    (1)/(sin3alpha)[sin^(3)alpha+sin^(3)((2pi)/(3)+alpha)+sin^(3)((4pi)/(3)+alpha)] is equal to

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