Question

Prove that cos θ + cos ($\frac{2\pi}{3}$ + θ) + cos ($\frac{4\pi}{3}$ + θ) = 0.

Answer 1

Answer:

0

Step-by-step explanation:

Formula used:

cos(A+B) = cosA cosB - sinA sinB

Now

cos∅ + cos(2∏/3 +∅) + cos( 4∏/3 +∅)

= cos∅ + cos2∏/3 cos∅ - sin2∏/3 sin∅

+ cos4∏/3 cos∅ - sin4∏/3 sin∅

= cos∅ + (-½)cos∅ - (√3⁄2) sin∅

+ ( -½)cos∅ - (- √3⁄2) sin∅

= cos∅ + (-½)cos∅ - (√3⁄2) sin∅

+ ( -½)cos∅ +(√3⁄2)sin∅

= cos∅ - cos∅- (√3⁄2) sin∅

+ (√3⁄2)sin∅

= 0

I hope this answer helps you