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

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Answer 1 · 2018-06-12T02:33:14

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

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

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

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

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

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

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

= $1^2$

= $1$

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