How do you prove $cos4x=1-2sin^2(2x)$ ?

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Answer 1 · 2016-01-08T11:31:06

using trig. identities.

by using double angle formula .

we can write that $cos4x = cos^ 2 2x - sin^2 2x$

if we use the identity that $cos^2 2x = 1 - sin^2 2x$

then placing this into the above gives

$cos 4x = (1 - sin^2 2x ) - sin^2 2x$

removing the bracket gives

$cos 4x = 1 - sin^2 2x - sin^2 2x$

$rArr cos 4x = 1 - 2sin^2 2x$

How do you prove cos4x=1-2sin^2(2x)cos4x=1-2sin^2(2x)?