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Prove that 4(cos ^(3) 10^(@) + sin ^(3) ...

Prove that `4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin 20^(@)).`

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i) Prove that: cos^(3)2A+3cos2A = 4(cos^(6)A-sin^(6)A) ii) Prove that: 4(cos^(3)10^(@) + sin^(3)20^(@)) = 3(cos10^(@)+sin20^(@))

4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

What is the value of (cos 10 ^(@) + sin 20^(@))/( cos 20^(@) - sin 10 ^(@))?

Prove that (cos ^(3) A - sin ^(3) A)/( cos A - sin A ) = (2 + sin 2 A)/( 2 ).

Prove that sin 20^(@) sin 40^(@) sin 80^(@) = (sqrt3)/(8).

Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2

Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2

Prove that : (cos^(3) A + sin^(3) A)/ (cos A + sin A) + (cos^(3) A - sin^(3) A)/(cos A - sin A) = 2

(1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

Prove that : (i) sin42^(@)cos48^(@)+sin48^(@)cos42^(@)=1 (ii) cos70^(@)cos20^(@)-sin70^(@)sin20^(@)=0

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: "sin"20^0"sin"40^0"sin"60^0"sin"80^0=3/(16)

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  2. prove sin(5theta) = 16sin^5(theta)-20sin^3(theta)+5sin(theta)

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  3. Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin...

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  4. Prove the following identity: cos^3thetasin3theta+sin^3thetacos3theta=...

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  5. Prove the following identity: \ t a nthetat a n(theta+60^0)+t a ntheta...

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

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

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  8. Prove the following identity: cot A+cot(60^0+A)+cot(120^0+A)=3cot3A

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  9. Prove that: sin^3A+sin^3((2pi)/3+A)+sin^3((4pi)/3+A)=-3/4sin3Adot

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  10. Prove that: |costhetacos(60^0-theta)cos(60^0+theta)lt=1/4 for all valu...

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

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

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

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

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

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

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

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

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

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

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