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If y=(cosx+secx)^2+(tanx+cotx)^2 then th...

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

A

7

B

3

C

9

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`y=(sin^2x-cos^2x0+2(sinxcosecx+cosxsecx)+sec^2x+cosec^2x`
`=5+2+tan^2x+cot^2x`
`=7+(tanx-cotx)^2+2`
`:. t_("min")=9`
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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. If abs(cos theta{sin theta+sqrt(sin^2theta+sin^2alpha)})lek, then the ...

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  15. In which of the following intervals the inequality, sinx < cos x < tan...

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  16. Th range of k for which the inequaliity kcos^2x-kcosx+1>=0 AA x in(-o...

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  17. The value of cos(pi/7)+cos((2pi)/7)+cos((3pi)/7)+cos((4pi)/7)+cos((5pi...

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  18. The numerical value of tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)is equal t...

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  19. The expression 3{sin^4((3pi/2)-alpha)+sin^4(3pi-alpha)} -2{sin^6(pi/2+...

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  20. The value of the expression log10(tan6^@)+log10(tan12^@)+log10(tan18^@...

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