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If sinx+sin^2x=1, then find the value of...

If `sinx+sin^2x=1`, then find the value of `cos^(12)x +3cos^(10)x + 3 cos^8x + cos^6x-1 `

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The correct Answer is:
3
We have `sinx+sin^2x=1`
`or sinx=1-sin^2xorsinx=cos^2x`
Now, `cos^12x+3sin^10x+3sin^4x+sin^3x-2`
`=sin^6x+3sin^5x+3sin^4x-2`
`=(sin^2x)^3+3(sin^2x)^2sinx+3(sin^2x)`
`(sinx)^2+(sinx)^3-2`
`=(sin^2x+sinx)^3-2=(1)^3-2=-1`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
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  2. Which of the following is not the quadratic equation whose roots are c...

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  3. If sinx+sin^2x=1, then find the value of cos^(12)x +3cos^(10)x + 3 cos...

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  4. 3(sintheta-costheta)^(4)+6(sintheta+costheta)^(2)+4(sin^(6)theta+cos^(...

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  5. If sinx+sin^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

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  6. (1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=

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  7. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

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  8. A circle is drawn in a sectore of a larger circle of radius r, as show...

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  9. A right triangle has perimeter of length 7 and hypotenuse of length 3....

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  10. Given that the side length of a rhombus is the geometric mean of the ...

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  11. Which of the following is correct?

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  12. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

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  13. if sin^2theta=(x^2+y^2+1)/(2x) then x must be

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  14. sec^2 x=(4xy)/(x+y)^2 is true if and only if

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  15. If sintheta1+sintheta2+sintheta3=3," then "costheta1+costheta2+costhet...

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

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

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

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

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