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If sinx+siny+sinz+sinw=-4" then the valu...

If `sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^200z+sin^100w` is

A

`sin^400x.sin^300y.sin^200z.sin^100w`

B

`sinx.siny.sinz.sinw`

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
`sinx+siny+sinz+sinw=-4`
`rArrsinx=siny=sinz=sinw`
So,`sin^400x+sin^300y+sin^200x+sin^100w`
`=-(-1)^400+(-1)^300+(-1)^200+(-)^100=4`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
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  2. If sintheta1+sintheta2+sintheta3=3," then "costheta1+costheta2+costhet...

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  3. If sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^20...

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  4. The minimum value of the expression sin alpha + sin beta+ sin gamma, ...

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  5. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

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  6. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)(2sin^2 180^0-1)...

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  7. If sinA=sin^2B and 2cos^2A=3cos^2B then the triangle ABC is

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  8. If sintheta+costheta=1/5and 0lethetaltpi" then "tantheta is

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  9. If piltalphalt(3pi)/2lt" then "sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1...

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  10. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

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  11. The least value of 2sin^2theta+3cos^2theta is

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  12. The greatest value of sin^4theta+cos^4theta is

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  13. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

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  14. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

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  15. Range of f(theta)=cos^2theta(cos^2theta+1)+2 sin^2theta is

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  16. If 0<theta<pi, then minimum value of 3sintheta+cos e c^3theta is 4 (b)...

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  17. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

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  18. The set of values of lambda in R such that sin^2theta+costheta=lambda...

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  19. Let A=sin^8theta+cos^14theta, " then "A("max") is

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  20. Minimum value of y=256 sin^2x+324cosec^2x AA x inR is

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