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Prove that: a) sin(A+B+C) + sin(A-B-C)...

Prove that:
a) `sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC`
b) `cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC`

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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3H
  1. In DeltaABC,prove that: sin2A + sin2B-sin2C=4cosA cosB sinC

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  2. If A+B+C=pi, prove that : sinA+sinB+sinC= 4cos, A/2 cos, B/2 cos, C/2

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  3. In DeltaABC, prove that: a) (sin2A + sin2B + sin2C)/(sinA+sinB+sinC) ...

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  4. In a triangle ABCsin(B+2C)+sin(C+2A)+sin(A+2B)=4sin((B-C)/2)sin((C-A)/...

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  5. In DeltaABC, prove that: a) sin(A/2)+sin(B/2) +sin(C/2)=1+4sin((pi-A...

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  6. If A+B+C=pi/2, prove that: sin2A + sin2B+sin2C = 4cosA cosB cosC

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  7. Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4si...

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  8. If A+B+C=180, prove that: sinA+sinB+sinC=4cos(A/2)cos(B/2)cos(C/2...

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  9. If A+B+C=2S, prove that: sin(S-A)+sin(S-B)+sin(S-C)-sinS = 4sinA/2si...

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  10. If DeltaABC, prove that: a) sin^(2)A+sin^(2)B-sin^(2)C=2sinAsinBcosC...

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  11. If A+B+C=180^0, prove that : cos^2 (A/2) + cos^2 (B/2) - cos^2 (C/2) =...

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  12. If A+B+C=pi, then prove that tanA/2.tanB/2 +tanB/2.tanC/2 + tanC/2. ta...

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  13. In DeltaABC, prove that: cotBcotC+cotCcotA+cotAcotB=1

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  14. In DeltaABC, prove that: tan2A + tan2B+tan2C=tan2Atan2Btan2C

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  15. Prove that: (tan(alpha-beta)+tan(beta-lambda)+tan(lambda-alpha) = ta...

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  16. In DeltaABC, prove that: tanBtanC+tanCtanA+tanAtanB=1+secAsecBsecC

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  17. In DeltaABC, prove that: cotA+cotB+cotC = cotAcotBcotC+"cosec"A"cose...

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  18. If x+y+z=xyz, prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^...

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