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

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

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

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

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

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

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

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

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  7. Find the values of cos pi/8

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

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

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

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  11. Prove that: cos(pi/7)cos((2pi)/7)cos((4pi)/7)=-1/8

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  12. If alpha and beta are distinct roots of acostheta+b sintheta=c , prove...

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  13. Prove that: sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

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  14. Prove that: Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A

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  15. If tanA=1/7a n d tanB=1/3 , show that cos2A=sin4Bdot

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  16. If 2t a nalpha/2=tan(beta/2) , prove that cosalpha=(3+5cosbeta)/(5+3c...

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  17. If acos2theta+bsin2theta= c, alpha and beta as its roots , then prove ...

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  18. If cosalpha+cosbeta=0=s inalpha+s inbeta, then prove that cos2alpha+co...

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  19. Prove that: 15sin(5pi)/(12)+15cos(5pi)/(12)-20sin^3(5pi)/(12)-20cos(5p...

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  20. Prove that: sin(pi/5)sin( (2pi)/5)sin(3pi/5)sin(4pi/5)=5/(16)

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