Question

`cos^2(2x)+sin^2(2x)=?` what value is this equal to?

Answer 1

`cos^2(2x)+sin^2(2x)=1`

Explanation:

Remember the equation `cos^2x+sin^2x=1`?
Well the `x` refers to any number so if your number is `2x`, then `cos^2 2x+sin^2 2x=1`

You can also prove this by using the double angle formula

`cos^2(2x)+sin^2(2x)`

=`(cos^2x-sin^2x)^2+(2sinxcosx)^2`

=`cos^4x-2sin^2xcos^2x+sin^4x+4sin^2xcos^2x`

=`cos^4x+2sin^2xcos^2x+sin^4x`

=`(cos^2x+sin^2x)^2`

=`1^2`

=`1`