How do I solve this?
If cos x= 3/5, find the exact value of cos 2x
have you come across the identity
cos 2x = 2cos^2 x - 1
we can just apply this here.
cos 2x = 2(3/5)^2 - 1
= -7/25
No I have not come across that before.
then probably
cos2x = cos^2 x - sin^2 x
(I replaced sin^2 x with 1-cos^2 x to get the one I used)
Your question fits right into the application of the double and half angle formulas, and without these your question becomes a mess.
Oh I get it now. thanks for your help.
To solve the problem, we can use the double angle identity for cosine. The double angle identity for cosine states that cos 2x = 2(cos^2 x) - 1.
First, let's find the value of cos^2 x using the given information that cos x = 3/5.
To find cos^2 x, we square the value of cos x:
(cos x)^2 = (3/5)^2 = 9/25.
Next, substitute the value of cos^2 x into the double angle identity:
cos 2x = 2(cos^2 x) - 1
cos 2x = 2(9/25) - 1
cos 2x = 18/25 - 1
cos 2x = (18 - 25)/25
cos 2x = -7/25.
Therefore, the exact value of cos 2x is -7/25.