It's been a while since I've done trig proofs. I know that cos &#x2061;<!-- ⁡ --> ( 2 &#

Ellie Benjamin

Ellie Benjamin

Answered question

2022-07-09

It's been a while since I've done trig proofs. I know that
cos ( 2 θ ) + cos ( 2 ( π 3 + θ ) ) + cos ( 2 ( 2 π 3 + θ ) ) = 0

Answer & Explanation

persstemc1

persstemc1

Beginner2022-07-10Added 18 answers

By a formula that is well known,
c o s ( A ) + c o s ( B ) = 2 c o s ( ( A + B ) / 2 ) c o s ( ( A B ) / 2 )Let B = 4 π / 3 + 2 θ. Then by the above,
c o s ( 2 θ ) + c o s ( 4 π / 3 + 2 θ ) = 2 c o s ( 2 θ + 2 π / 3 ) c o s ( 2 π / 3 ) = c o s ( 2 θ + 2 π / 3 )
The first formula used above must have been rote learnt or at least encountered in high school. It's use gives a 2 line proof as I have shown.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?