Asked by Anonymus
Prove that it is an identity: cos (4x)=8cos^4(x)-8cos^2(x)+1
Answers
Answered by
Reiny
Using the property : cos 2A = 2cos^2 A -1
cos(4x)
= 2cos^2 (2x) - 1 = 2(cos(2x))(cos(2x)) - 1 , using the same property again
= 2(2cos^2 x - 1)^2 - 1
= 2(4cos^4 x - 4cos^2 x + 1) - 1
= 8cos^4 x - 8cos^2 x + 1
= RS
cos(4x)
= 2cos^2 (2x) - 1 = 2(cos(2x))(cos(2x)) - 1 , using the same property again
= 2(2cos^2 x - 1)^2 - 1
= 2(4cos^4 x - 4cos^2 x + 1) - 1
= 8cos^4 x - 8cos^2 x + 1
= RS
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.