Question

Prove that:
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Answer 1

Answer:

Step-by-step explanation:

Cos(A - π) + Sin(A + π/2)

We know that Cos(A - B) = CosACosB - SinASinB

                        Sin(A+B) = SinACosB + CosASinB

=> CosACosπ - SinASInπ + SinACosπ/2 + CosASinπ/2

We know that Cos 90 = 0 and Cos180 = - 1 and Sin90 = 1 and Sin180 = 0.

=>  CosA(-1) + SinA(0) + SinA(0) + CosA(1)

=> - CosA + CosA

=> 0

= R.H.S

Hence proved.