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Prove that sinalpha+sin(alpha+(2pi)/3)+s...

Prove that `sinalpha+sin(alpha+(2pi)/3)+sin(alpha+(4pi)/3)=0`.

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PATHFINDER-TRANSFORMATION FORMULAE-QUESTION BANK
  1. Prove that (sinA+sinB)/(sinA-sinB)=tan((A+B)/2)cot((A-B)/2)

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  2. Prove that (sinA+sin3A)/(cosA+cos3A)=tan2A.

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  3. Evaluate:sin75^@ cdot cot15^@

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  4. Prove that (sinA+sinB)/(cosA+cosB)=tan((A+B)/2)

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  5. Prove that2"sin"(5pi)/(12)"cos"(pi)/(12)=(sqrt3+2)/2

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  6. If sin(theta+alpha)/(cos(theta-alpha))=(1-m)/(1+m) Prove that tan(pi/4...

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  7. If cosecA+secA=cosecB+secB Prove that tanAtanB=cot((A+B)/2).

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  8. Prove that (sin(theta+phi)-2sintheta+sin(theta-phi))/(cos(theta+phi)-2...

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  9. Show thatsinalpha+sinbeta+singamma-sin(alpha+beta+gamma)=4sin ((alpha+...

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  10. Prove that cos10^@cos30^@cos50^@cos70^@=3/(16).

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  11. Prove that sin20^@sin40^@sin80^@=sqrt3/8

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  12. Prove thatsin10^@sin50^@sin60^@sin70^@=sqrt3/(16)

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  13. Prove that tan20^@tan30^@tan40^@tan80^@=1

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  14. Prove that (sin5A-sin7A+sin8A-sin4A)/(cos4A+cos7A-cos5A-cos8A)=cot6A

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  15. Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-bet...

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  16. Prove that sinalpha+sin(alpha+(2pi)/3)+sin(alpha+(4pi)/3)=0.

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  17. 2 cos ""pi/13 cos "" (9pi)/( 13) + cos "" (3pi)/(13) + cos " (5pi)/( 1...

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  18. Show that tan20^@tan40^@tan80^@=sqrt3

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  19. If cosA+cosB=1/2and sinA+sinB=1/4Prove that tan((A+B)/2)=1/2

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  20. If sin2A=lamdasin2B.Prove that tan(A+B)/(tan(A-B))=(lamda+1)/(lamda-1)

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