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Show that 3(sin^4x+cos^4x)-2(sin^6x+cos^...

Show that `3(sin^4x+cos^4x)-2(sin^6x+cos^6x)=1`.

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`2(sin^6x+cos^6x)-3(sin^4x+cos^4x)+1`
`=2[(sin^2x)^3+(cos^2x)^(3)]-3(sin^4x+cos^4x)+1`
`=2[(sin^2x+cos^2x)^3-3sin^2xcos^2x(sin^2x+cos^2x)]-3[(sin^2x+cos^2x)^2-2sin^2xcos^2x]+1`
`=2[1-3sin^2xcos^2x]-3[1-2sin^2xcos^2x]+1=0`
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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Show that 3(sin^4x+cos^4x)-2(sin^6x+cos^6x)=1.

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  2. The circular wire of diameter 10 cm is cut and placed along the circum...

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  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

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  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

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  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

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  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

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  12. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

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  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

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  17. Which of the following is true ?

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  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

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  19. Which of the following is greatest ?

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  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

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  21. Which of the following is not correct ?

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