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The minimum value of sin^4theta+cos^4the...

The minimum value of `sin^4theta+cos^4theta` is

A

`1//2`

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^4theta+cos^4=(sin^2theta+cos^2theta)^2-2sin^2thetacos^2theta`
`=1-2sin^2thetacos^2thetale1`
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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

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  2. The least value of 3sin^2theta+4cos^2theta is

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  3. The minimum value of sin^4theta+cos^4theta is

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

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  6. Range of f(theta)=cos^2theta(cos^2theta+1)+3sin^2theta is

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

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

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

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  10. Let A=sin^6theta+cos^8theta, " then "A("max") is

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  11. Minimum value of y=25sin^2x+36cos e c^2xAAx in R is

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  12. If aa n db are positive quantities such that a > b , the minimum value...

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  13. If y=(cosx+secx)^2+(tanx+cotx)^2 then the minimum value of y,AAx in R,...

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  14. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

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  15. If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, th...

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  16. If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of va...

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  17. If the inequality sin^2x+acosx+a^2>1+cosx holds for any x in R , then...

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  18. If 0 lt alpha lt pi/2, then sqrt(2cotalpha+1/(sin^2alpha)) is equal t...

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  19. The value of sectheta/sqrt(1+tan^2theta)+(cosectheta)/(sqrt(1+cot^2th...

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  20. The minimum value of the function f(x)=sinx/(sqrt(1-cos^2x))+cosx/sqrt...

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