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Prove the following identity: \ t a nthe...

Prove the following identity: `\ t a nthetat a n(theta+60^0)+t a nthetatan(theta-60^0)+tan(theta+60^0)tan(theta-60^0)=-3`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
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  3. Prove the following identity: \ t a nthetat a n(theta+60^0)+t a ntheta...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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