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Prove that: (costheta)/(1+sintheta)=tan(...

Prove that: `(costheta)/(1+sintheta)=tan(pi/4-theta/2)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta

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  2. Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

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  3. Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

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  4. Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

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  5. Prove that : cos4x=1-8sin^2xcos^2x

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  6. Prove that: (sin5x-2sin3x+sin x)/(cos5x-cos x)=tanx

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  7. Prove that : (sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx

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  8. Express each of the following as the sum or difference of sines and ...

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  9. Show that sqrt(3)\ cos e c\ 20^0-sec20^0=4.

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  10. Prove that: tan4theta=(4t a ntheta(1-tan^2theta))/(1-6tan^2theta+tan^4...

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  11. If tanx=3/4, pi < x < (3pi)/2 , find the values of sinx/2, cosx/2 and...

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  12. Prove that : cos 20^0cos 40^0cos 60^0cos 80^0=1/(16)

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  13. Prove that : cos(pi/7)cos((2pi)/7) cos((3pi)/7)=1/8

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  14. Show that: sin 50^0cos95^0=(sqrt(2)sin35^0-1)/(2sqrt(2))

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  15. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15...

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  16. sin(pi/18)*sin(5pi/18)*sin(7pi/18)

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  17. Prove:cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)co...

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  18. If sinalpha+sinbeta=a and cosalpha+cosbeta=b prove that: cos(alpha-bet...

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  19. If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)=

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  20. Prove that sqrt((1-cos2theta)/(1+cos2theta))=tantheta where tantheta>0

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