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Ellie Padilla
Mathematics
14 July, 04:08
Verify the identity.
cos 4u = cos22u - sin22u
+2
Answers (
1
)
Ricardo Marks
14 July, 04:26
0
To verify the above we proceed as follows:
cos 2u = (cos u) ^2 - (sin u) ^2
hence,
cos 4u = (cos 2u) ^2 - (sin u) ^2
By Pythagorean identity:
(sin 2u) ^2 + (cos 2u) ^2=1
thus;
(sin 2u) ^2=1 - (cos 2u) ^2
hence
(cos 2u) ^2 - (1 - (cos 2u) ^2)
= (cos 2u) ^2-1 + (cos u) ^2
2 (cos 2u) ^2-1
=cos (4u)
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