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The value of (sin5alpha-sin3alpha)/(cos5...

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

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we know ,
`sinC - sinD = 2sin((C-D)/2) sin((C+D)/2)`
`cosC + cosD = 2cos((C+D)/2)cos((C-D)/2)`
`L.H.S. = (sin5alpha-sin3alpha)/(cos5alpha+2cos4alpha+cos3alpha)`
`=>(2sin((5alpha-3alpha)/2) sin((5alpha+3alpha)/2))/(2cos((5alpha+3alpha)/2)cos((5alpha-3alpha)/2+2cos4alpha2q)`
`=(2sinalphacos4alpha)/(2cos4alphacosalpha+2cos4alpha)`
`=sinalpha/(1+cos alpha)`
...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

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

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

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  4. If costheta=1/2(a+1/a),cos3theta=lambda(a^3+1/(a^3)),t h e nlambda= ...

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

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

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

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

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

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

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  11. Find the values of cospi/8

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

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  13. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a...

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

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

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  16. If alpha and beta are distict roots of acostheta+b sintheta=c , prov...

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  17. sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

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  18. Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A

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  19. If tanA=1/7a n dtanB=1/3 , show that cos2A=sin4Bdot

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

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