Is cos^4(x)+sin^2(x)=sin^2(+cos^2(x)) ?

The answer to whether cos^4(x)+sin^2(x)=sin^2(+cos^2(x)) is False

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prove cos^4(x)+sin^2(x)=sin^2(+cos^2(x))

prove

cos^{4} (x) + sin^{2} (x) = sin^{2} (+ cos^{2} (x))

False

Solution steps

cos^{4} (x) + sin^{2} (x) = sin^{2} (cos^{2} (x))

Show that the two sides are not equal

For

cos^{4} (x) + sin^{2} (x) = sin^{2} (cos^{2} (x))

plug in

x = 0

cos^{4} (0) + sin^{2} (0) = 1

cos^{4} (0) + sin^{2} (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 1^{4} + 0^{2}

Simplify

= 1

sin^{2} (cos^{2} (0)) = 0.70807 \dots

sin^{2} (cos^{2} (0))

Refine to a decimal form

= 0.70807 \dots

The two sides are not equal

\Rightarrow False

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