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3(sintheta-costheta)^(4)+6(sintheta+cost...

`3(sintheta-costheta)^(4)+6(sintheta+costheta)^(2)+4(sin^(6)theta+cos^(6)theta)=?`

A

11

B

12

C

13

D

14

Text Solution

Verified by Experts

The correct Answer is:
C
`3(sintheta-costheta)^4+6(sintheta-costheta)^2+4(sin^6theta+cos^6theta)`
`=3[sin^4theta+cos^4theta-4sin^3thetacostheta`
`+6sin^2cos^2theta-4sinthetacos^3theta]+6[1+2sinthetacostheta]`
`+4[sin^4theta+cos^4theta-sin^2thetacos^2theta]`
`=7[sin^4theta+cos^4theta]+14sin^2thetacos^2theta-12 sinthetacostheta+6+12sinthetacostheta`
`=7(sin^2theta+cos^2theta)^2+6=13`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
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  2. If sinx+sin^2x=1, then find the value of cos^(12)x +3cos^(10)x + 3 cos...

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

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

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  5. (1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=

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

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

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

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

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  10. Which of the following is correct?

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

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

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

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

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

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

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

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

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

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