Question

expand cos(A+B+C) and
hence prove that cosA cosB cosC=sinA sinB cosC+ sinB sinC cosA +sinC sinA cosB
If A+B+C=90 i.e (Pi/2)

Answer 1

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Answer 2

Answer:

Taking A+B=X and C=Y

We get Cos(x + y) = Cos x Cos y - Sin x Sin y

i.e Cos (A+B+C) = Cos (A+B) Cos C - Sin (A+B) Sin C

= (Cos A Cos B - Sin A Sin B ) Cos C - [ Sin A Cos B + Cos A Sin B ] Sin C

Cos(A+B+C) = Cos A Cos B Cos C -Sin A Sin B Cos C -Sin A Cos B Sin C - Cos A Sin B Sin C

If (A+B+C) = π/2 then Cos (A+B+C)=0

Cos A Cos B Cos C -Sin A Cos B Sin C -Cos A Sin B Sin C =0

Cos A Cos B Cos C = Sin A Sin B Cos C +Sin B Sin C Cos A + Sin C Sin A Cos B