Question

cos^2(pi/9) - sin^2(pi/9) Use identities to simplify. (Half angle and double angle)

Answer 1

Do you know your double angle formulas?

Answer 2

yes but idk how yo use it with this problem

Answer 3

Oh okay. Well cos(2A) = cos^2A - sin^2A or 1 - 2sin^2 A or 2cos^2A - 1, sin (2A) = 2sinAcosA and tan (2A) = 2tanA/1-tan^2A which formula do you think matches?

Answer 4

cos(2A) = cos^2A - sin^2A

Answer 5

Good and your A in this case is?

Answer 6

pi/6

Answer 7

2 times pi/9 is pi/6

Answer 8

sorry got that wrong

Answer 9

Actually \[\frac{ 2\pi }{ 9 }\] can't be reduced. Since it was given to you in cos^2A -sin^2A . it becomes cos (2A) , which is just cos (2*pi/9).

Answer 10

ok now do u plug in>

Answer 11

Well is your question looking for an answer or to just leave it as \[\cos \frac{ 2\pi }{ 9 }\] ?

Answer 12

yeah it is asking for simplification. And it looks like it has been simplified. Thank you :)

Answer 13

No problem! (: