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Prove that: sin A sin(60-A)sin(60+A)=1/4...

Prove that: `sin A sin(60-A)sin(60+A)=1/4sin3Adot`

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To prove that \( \sin A \sin(60^\circ - A) \sin(60^\circ + A) = \frac{1}{4} \sin 3A \), we will start with the left-hand side and manipulate it step by step. ### Step 1: Rewrite the left-hand side We start with the expression: \[ LHS = \sin A \sin(60^\circ - A) \sin(60^\circ + A) \] ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that cos6x=32cos^6x-48cos^4x+18cos^2x-1

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  2. Prove that : cos Acos(60-A)cos(60+A)=1/4cos3A

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  3. Prove that: sin A sin(60-A)sin(60+A)=1/4sin3Adot

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  4. Prove that: "sin"20^0"sin"40^0"sin"60^0"sin"80^0=3/(16)

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

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  6. Prove the following identity: 4(cos^3 10^0+sin^3\ \ 20^0)=\ 3\ (cos 10...

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  7. Prove the following identity: cos^3thetas in3theta+sin^3thetacos3theta...

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  8. Prove the following identity: tan θ tan(60^@ +θ)tan(60^@ −θ)=]ta...

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  9. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3ALet's use the sum...

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

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

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

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  13. Maximum value of |costhetacos(60^0-theta)cos(60^0+theta) for all valu...

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

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  15. Prove that cos(2pi)/(15)cos(4pi)/(15)cos(8pi)/(15)cos(14pi)/(15)=1/(16...

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

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

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

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

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

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