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Prove that, a^(3)sin(B-C)+b^(3)sin(C-A...

Prove that,
`a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0`

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Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove that, (tanA+tanB)/(tanA-tanB)=(sin(A+B))/(sin(A-B))

Prove that, sin^(3)A+sin^(3)((2pi)/(3)+A)+sin^(3)((4pi)/(3)+A)=-(3)/(4)sin3A

For any triangle ABC, prove that : (sin(B-C))/(sin(B+C))=(b^(2)-c^(2))/(a^(2))

Prove that, sin^(2)A+sin^(2)B+cos^(2)(A+B)+2sinAsinBcos(A+B)=1

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KUMAR PRAKASHAN-TRIGONOMETRIC FUNCTIONS -PRACTICE WORK
  1. Prove that, 2(asin^(2)((C)/(2))+csin^(2)((A)/(2)))=c+a-b

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  2. Prove that, tan((A)/(2)+B)=(c+b)/(c-b)tan((A)/(2))

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  3. Prove that, a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0

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  4. Prove that, cot""(pi)/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

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  5. Prove that, tan""(pi)/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

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  6. Prove that, 4sin27^(@)=sqrt(5+sqrt(5))+sqrt(3-sqrt(5))

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  7. If alpha and beta are roots of the equation acostheta+bsintheta=c then...

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  8. If alpha and beta are roots of the equation acostheta+bsintheta=c then...

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  9. If costheta=a then show that cos^(2)((theta)/(2)) and sin^(2)((theta)/...

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  10. Prove that, (2costheta+1)(2costheta-1) (2cos2theta-1)(2cos4theta-1)=...

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  11. If DeltaABC is a right angle triangle then prove that cos^(2)A+cos^(2)...

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  12. If cosalpha=(3)/(5),cosbeta=(5)/(13),0ltalpha,betalt(pi)/(2) then find...

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  13. Prove, sin6^(@).sin(42^(@)).sin(66^(@)).sin(78^(@))=(1)/(16) .

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  14. Prove that 2tanbeta+cotbeta=tanalphaimplies2tan(alpha-beta)=cotbeta.

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  15. If theta+beta=alphaandsintheta=ksinbeta then prove that tantheta=(ksin...

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  16. If asintheta=bsin(theta+(2pi)/(3))=csin(theta+(4pi)/(3)) then prove th...

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  17. If cosalpha=(-5)/(13),(pi)/(2)ltalphaltpiandtanbeta=(4)/(3),piltbetalt...

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  18. Solve : sqrt(2)sectheta+tantheta=1

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  19. Solve : 4costheta-3sectheta=tantheta

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  20. If costheta=(cosalphacosbeta)/(1-sinalphasinbeta) then prove that ta...

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