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If sin x+cosec\ x=2, then write the valu...

If `sin x+cosec\ x=2,` then write the value of `sin^n x+cos e c^n xdot`

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We have `sinx+cosecx=2`
`=>sinx+1/sinx=2`
This means `x=90^@`as max value of `sinx=1` such that `1+1=2`
Now, for any n, we have `sin^n90^@+cosec^n90^@=1^2+1^2=2`
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Write the maximum value of sin(cosx)dot

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  2. If sin x=cos^2x ,\ then write the value of cos^2x\ (1+cos^2x)dot

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  3. If sin x+cosec\ x=2, then write the value of sin^n x+cos e c^n xdot

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  4. If sintheta1+sintheta2+sintheta3=3, then costheta1+costheta2+costheta...

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  11. Write the least value of cos^2theta+sec^2thetadot

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  12. If x=sin^(14)theta+cos^(20)theta , then write the smallest interval in...

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  13. If 3sintheta+5costheta=5, then write the value of 5sin theta-3costheta...

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  14. If sectheta=x+1/(4x) , then s e ctheta-t a ntheta is equal to -2x ,1/(...

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  15. If pi/2 < theta < (3pi)/2 then sqrt ((1-sin theta)/(1+sin theta))= a....

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  16. If pi lt theta lt 2pi then sqrt ((1+cos theta)/(1-cos theta))= a. co...

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  17. If sec theta= x+1/(4x) then sec theta+ tan theta= a, x, 1/(x), b. 2x, ...

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  18. If pi/2ltthetaltpi, then sqrt((1-sintheta)/(1+sintheta))+sqrt((1+sinth...

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  19. If tan theta+sectheta=sqrt(3),\ 0<theta<pi, then theta is equal to (5p...

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  20. If t a ntheta=-1/(sqrt(5)) and theta lies in the IVB quadrant, then th...

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