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Prove that cos(A+B)cosC - cos(B+C)cosA = sinBsin(C-A)

Prove that cos(A+B)cosC - cos(B+C)cosA = sinBsin(C-A)

Grade:12

2 Answers

YASH AHUJA
28 Points
3 years ago
= (cosAcosB - sinAsinB)cosC - (cosBcosC - sinBsinC)cosA= cosAcosBcosC - sinAsinBcisC - cosAcosBcosC + sinBsinCcosA= sinBsinCcosA - sinBsinAcosC= sinB(sinCcosA - cosCsinA)= sinBsin (C- A)
Shiva
14 Points
one year ago
= (cosAcosB - sinAsinB)cosC - (cosBcosC - sinBsinC)cosA
= cosAcosBcosC - sinAsinBcisC - cosAcosBcosC + sinBsinCcosA
= sinBsinCcosA - sinBsinAcosC= sinB(sinCcosA - cosCsinA)
= sinBsin (C- A)

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