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Prove that: cos^2theta=cos^2alpha thent...

Prove that: `cos^2theta=cos^2alpha` then`theta=npi+-alpha,n in Z`

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Given:
`cos^2theta=cos^2alpha`
Using Identity
`cos2theta=2cos^2theta-1`
`1+cos2theta=2cos^2theta`
`cos^2theta=(1+cos2theta)/2`
`(1+cos2theta)/2=(1+cos2alpha)/2`
`cos2theta=cos2alpha`
`2theta=2npi pm 2alpha`
`theta=npi pm alpha`
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RD SHARMA-TRIGONOMETRIC EQUATIONS-Solved Examples And Exercises
  1. Write the values of x in[0,pi] for which sin2x ,1/2a n dcos2x are in A...

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  2. Prove that: tan^2theta=tan^2alpha ,theta=npi+-alpha,n in Z

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  3. Prove that: cos^2theta=cos^2alpha thentheta=npi+-alpha,n in Z

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  4. Find the general solutions of the following equations: (i) sin 2the...

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  5. Find the general solutions of the following equations: (i) cos3theta=0...

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  6. Find the general solutions of the following equations: tan2theta=0 ...

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  7. Prove that the general solution of sin"theta"=sin"alpha" is given by :...

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  8. Prove that the general solution of costheta=cosalpha is given by : the...

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  9. Prove that the general solution of tantheta=tanalpha is given by : the...

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  10. Solve the following trigonometric equations: s intheta/2=-1 (ii) cos(3...

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  11. Solve that following equation: cottheta+t a ntheta=2

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  12. Write the number of solutions of the equation t a nx+s e cx=2cosx in t...

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  13. The number of values of x in the interval 0,5pi satisfying the equatio...

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  14. If a is any real number, the number of roots of cotx-t a nx=a in the f...

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  15. Solve: sqrt(3) costheta+sintheta=sqrt(2)

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  16. If cosx=k has exactly one solutions in [0,2pi] , then write the values...

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  17. Write the number of points in intersection of the curves 2y=-1and y=co...

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  18. Find the general solutions of the following equation: sintheta=(sqrt(3...

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  19. Find the general solutions of the following equation: 2\ sin\ theta+1=...

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  20. Find the general solutions of the following equation: cos e c\ theta=2

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