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If A + B + C = pi and cos A = cos B cos C, show that
tan A = tan B + tan C
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Answer:
Step-by-step explanation:
tan B + tan C = SinB/CosB + SinC/CosC
=> SinB.CosC + SinC.CosB / CosBCosC
//Given CosA = CosBCosC
// Sin(A+B) = SinACosB + CosASinB
= Sin(B+C) / CosA
// Given A + B + C = π => B + C = π - A
= Sin (π - A)/ CosA
= SinA/CosA
= TanA
= R,H,S
Hence proved.
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