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

Prove that `cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15))=1/(16)`

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To prove that \[ \cos\left(\frac{2\pi}{15}\right) \cos\left(\frac{4\pi}{15}\right) \cos\left(\frac{8\pi}{15}\right) \cos\left(\frac{16\pi}{15}\right) = \frac{1}{16}, \] we will follow a systematic approach using trigonometric identities. ...
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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: |costhetacos(60^0-theta)cos(60^0+theta)lt=1/4 for all valu...

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  2. Prove that: sin(pi/5) sin2pi/5 sin3pi/5 sin4pi/5=5/16

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  3. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15...

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  4. Prove that: sin 12^0sin 48^0sin 54^0=1/8dot

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  5. The value oif the expressin (1+cospi/10)(1+cos(3pi)/10)(1+cos(7pi)/10)...

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  6. Prove that ; 4 sin 27^@=(5+sqrt(5))-sqrt((3-sqrt(5))) we have

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  7. Prove that : sin^2(72^@) - sin^2 (60^@) = (sqrt5 - 1)/8

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

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  9. Prove that: sin^2 42^0-cos^2 78^0=(sqrt(5)+1)/8

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  10. Prove that: cos 78^0cos 42^0cos 36^0=1/8

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  11. Show that cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/1...

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  12. Prove that cos6^@ . cos42^@. cos66^@ cos78^@= 1/16

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  13. Prove that: sin6^0sin42^0sin 66^0sin 78^0=1/(16)

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  14. Prove that: sin36^0s in 72^0s in 108^0s in 144^0=5/(16)dot

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  15. If cos4x=1+ksin^2x cos^2x , then write the value of kdot

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  16. If tanx/2=m/n ,\ then write the the value of msinx+n\ cos xdot

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  17. If pi/2 < theta < (3pi)/2 then write the value of sqrt((1+cos2theta)...

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  18. If pi/2<theta<pi,then write the value of sqrt(2+sqrt(2+2cos2theta)) in...

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  19. If pi/2<theta<pi , then write the value of sqrt((1-cos2theta)/(1+cos2t...

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  20. If pi<theta<(3pi)/2 , then write the value of sqrt((1-cos2theta)/(1+co...

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