Question

prove cos A + cos(120-A) + cos(120+A) = 0

Answer 1

hay!!



Dear user -



PROVE THAT COSA + COS(120-A)+COS(120+A)=0



❄here is ur answer ❄


LHS=>


CosA+Cos(120-A) + Cos(120+A)



$\frac{cosa + 2cos(120 - a + 120 + a)}{2cos(120 - a - 120 - a)}$

we know that formula


( cos C+ cosD = 2cos (C+D)/2.cos (C-D) /2)


=> cosA+2cos120 cos-A


=> cosA+2cos (180-60) cosA


=> cosA+2(-cos60) cosA


$cosa - 2 \times \frac{1}{2}cosa$

=> cosA-cosA


=> 0

Hence proved


I hope it's help you

Answer 2

Answer:

CosA+cos(120+A)+cos(120-A)

=CosA+2cos120cosA

[cos(A+B)+cos(A-B)=2cosAcosB]

=cosA+2cos(180-60)cosA

=CosA-2cos60cosA

=cosA-2(1/2)cosA

=cosA-cosA

=0