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show that cos^2(pi/9)+cos^2((2pi)/9)+cos...

show that `cos^2(pi/9)+cos^2((2pi)/9)+cos^2((4pi)/9)=3/2`

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UNITED BOOK HOUSE-TRIGONOMETRY-EXERCISE
  1. If (a^(2)-b^(2))sin theta+2 ab cos theta-(a^(2)+b^(2))=0, then prove t...

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  2. If (ax)/costheta+(by)/(sintheta)=a^2-b^2 and (axsintheta)/(cos^2theta)...

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  3. If cos^4x/cos^2y+sin^4x/sin^2y=1,show that cos^4y/cos^2x+sin^4y/sin^2x...

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  4. Show that 1/3le(sec^2theta-tantheta)/(sec^2theta+tantheta)le3

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  5. If sectheta=secalphassecbeta+tanalphatanbeta,show that tantheta=+-(sec...

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  6. If n^2sin^2(alpha+beta)=sin^2alpha+sin^2beta-2sinalphasinbetaxxcos(alp...

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  7. If (a+b)tan(theta-phi)=(a-b)tan(theta-phi)and acos2phi+bcos2theta=csho...

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  8. If (tan3alpha)/(tanalpha)=lambda,show that (sin3alpha)/(sinalpha)=(2la...

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  9. Prove that cos^8(pi/8)+cos^8((3pi)/8)+cos^8((5pi)/8)+cos^8((7pi)/8)=17...

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  10. Solve :sqrt(tanx+sinx)+sqrt(tanx-sinx)=2cosxsqrttanx

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  11. Solve :3^(sin2x+2cos^2x)+3^(1-sin2x+2sin^2x)=28

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  12. Solve :tan(x-pi/4)tanx tan(x+pi/4)=(4cos^2x)/(tan(x/2)-cot(x/2))

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  13. Solve :sqrt(2cos^2x+1)+sqrt(2sin^2x+1)=2sqrt2

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  14. Show that cos(pi/11)+cos((3pi)/11)+cos((5pi)/11)+cos((7pi)/11)+cos((9p...

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  15. In an acute angled triangle ABC, show that tan^2A+tan^2B+tan^2Cge9

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  16. If the medians of a triangle ABC makes anglesalpha,beta,gammawith each...

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  17. If cos^3theta=kcos(alpha-3theta)and sin^3theta=k sin(alpha-3theta),sho...

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  18. show that cos^2(pi/9)+cos^2((2pi)/9)+cos^2((4pi)/9)=3/2

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  19. Show that tan70^@+tan10^@-tan50^@=sqrt3

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  20. In /\ABC, show that the minimum value of tan^2 (A/2) + tan^2 (B/2) + t...

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