Is (cos(2x))/((cos(x)+sin(x)))=cos(x)-sin(x) ?

The answer to whether (cos(2x))/((cos(x)+sin(x)))=cos(x)-sin(x) is True

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prove (cos(2x))/((cos(x)+sin(x)))=cos(x)-sin(x)

prove

\frac{cos ( 2 x )}{( cos ( x ) + sin ( x ) )} = cos (x) - sin (x)

True

Solution steps

\frac{cos ( 2 x )}{cos ( x ) + sin ( x )} = cos (x) - sin (x)

Manipulating left side

\frac{cos ( 2 x )}{cos ( x ) + sin ( x )}

Rewrite using trig identities

= cos (x) - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (- \frac{3 π}{4})

cos (- \frac{π}{6})

sec (x) = 2, 0 \leq x \leq 2 π

sin (x) = - \frac{2}{2}

cos (4 π)

Is (cos(2x))/((cos(x)+sin(x)))=cos(x)-sin(x) ?
The answer to whether (cos(2x))/((cos(x)+sin(x)))=cos(x)-sin(x) is True