Is sin^2(2x)= 1/(2(1-cos^4(x))) ?

The answer to whether sin^2(2x)= 1/(2(1-cos^4(x))) is False

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prove sin^2(2x)= 1/(2(1-cos^4(x)))

prove

sin^{2} (2 x) = \frac{1}{2 ( 1 - cos ^{4} ( x ) )}

False

Solution steps

sin^{2} (2 x) = \frac{1}{2 ( 1 - cos ^{4} ( x ) )}

Show that the two sides are not equal

For

sin^{2} (2 x) = \frac{1}{2 ( 1 - cos ^{4} ( x ) )}

plug in

x = 1

sin^{2} (2 \cdot 1) = 0.82682 \dots

sin^{2} (2 \cdot 1)

Refine to a decimal form

= 0.82682 \dots

\frac{1}{2 ( 1 - cos ^{4} ( 1 ) )} = 0.54658 \dots

\frac{1}{2 ( 1 - cos ^{4} ( 1 ) )}

Refine to a decimal form

= 0.54658 \dots

The two sides are not equal

\Rightarrow False

\frac{( 1 - sin ( a ) )}{cos ( a )} = cos (a)

csc^{2} (x) (tan (x)) - (tan (x)) = cot (x)

sin^{4} (t) - cos^{4} (t) = 1 - 2 cos^{2} (x)

csc^{2} (A) = 1 + tan^{2} (A)

3 tan^{2} (x) = 3 (tan (x))^{2}

Is sin^2(2x)= 1/(2(1-cos^4(x))) ?
The answer to whether sin^2(2x)= 1/(2(1-cos^4(x))) is False