Question

Is Cos(A+B) =cosA+cosB.Justify
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Answer 1

$\Large{\underline{\underline{\sf{Given:}}}}$

• Cos(A+B) = CosA+CosB

$\Large{\underline{\underline{\sf{Required\; Response:}}}}$

Let's, Assume

Angle A = 60° & Angle B = 30°

As Per The Problem,

$\cos(60 + 30) = \cos(60) + \cos(30)$

$\cos(90) = \frac{1}{2} + \frac{ \sqrt{3} }{2}$

$0 = \frac{1 + \sqrt{3} }{2}$

Actually, $\Large{\bf{0 ≠ \frac{1+\sqrt{3}}{2}}}$

Consequently, Cos(A+B) ≠ CosA+CosB

$\pink{\bold{Cos(A+B) = CosA.CosB - SinA.SinB}}$

Done :)