Is sin^{0.5}(x)cos(x)-sin^{2.5}(x)cos(x)=cos^3(x)sin(x) ?

The answer to whether sin^{0.5}(x)cos(x)-sin^{2.5}(x)cos(x)=cos^3(x)sin(x) is False

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prove sin^{0.5}(x)cos(x)-sin^{2.5}(x)cos(x)=cos^3(x)sin(x)

prove

sin^{0.5} (x) cos (x) - sin^{2.5} (x) cos (x) = cos^{3} (x) sin (x)

False

Solution steps

sin (x) cos (x) - sin^{2.5} (x) cos (x) = cos^{3} (x) sin (x)

Show that the two sides are not equal

For

sin (x) cos (x) - sin^{2.5} (x) cos (x) = cos^{3} (x) sin (x)

plug in

x = 1

sin (1) cos (1) - sin^{2.5} (1) cos (1) = 0.14468 \dots

sin (1) cos (1) - sin^{2.5} (1) cos (1)

Refine to a decimal form

= 0.14468 \dots

cos^{3} (1) sin (1) = 0.13272 \dots

cos^{3} (1) sin (1)

Refine to a decimal form

= 0.13272 \dots

The two sides are not equal

\Rightarrow False

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

sin (\frac{2 π}{3}) = \frac{3}{2}

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

1 - tan^{2} (x) = sec^{2} (x)

\frac{cot ( x ) + 1}{csc ( x )} = cos (x) + sin (x)

Is sin^{0.5}(x)cos(x)-sin^{2.5}(x)cos(x)=cos^3(x)sin(x) ?
The answer to whether sin^{0.5}(x)cos(x)-sin^{2.5}(x)cos(x)=cos^3(x)sin(x) is False