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Prove that: cos18^0=(sqrt(10+2sqrt(5)))/...

Prove that: `cos18^0=(sqrt(10+2sqrt(5)))/4` .

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: cos36^0=(sqrt(5)+1)/4 .

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  2. Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8

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  3. Prove that: cos18^0=(sqrt(10+2sqrt(5)))/4 .

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  4. If t a ntheta/2=sqrt((1-e)/(1+e))tan(alpha/2), then cosalpha= (a) 1...

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  5. If cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2x is equal to

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  6. If alpha and beta are acute angles satisfying cos2alpha=(3cos2beta-1)/...

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  7. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

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  8. Prove that: cos^(2)48^(@)-sin^(2)12^(@)=(sqrt(5)+1)/(8)

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  9. The value of (sin5alpha-sin3alpha)/(cos5alpha+2cos4alpha+cos3alpha) is

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  10. If costheta=1/2(a+1/a),cos3theta=lambda(a^3+1/(a^3)), t ...

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  11. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

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  12. If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

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  13. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2thetacos2^...

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  14. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

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  15. Prove that: cos^2 48^0-sin^2 12^0=(sqrt(5)+1)/8

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  16. Find sin x/2 ,cos x/2 and tan x/2 of the following : tanx=-4/3,""x in...

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  17. Find the values of cos pi/8

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  18. Prove that: sin(pi/14)sin((3pi)/14)sin((5pi)/14)sin((7pi)/14)sin((9pi...

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  19. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)....(1+sec2^ntheta)...

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  20. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

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