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

The answer to whether (cos(x)-sin(x))^2=1-2cos(x)sin(x) is True

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

prove

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

True

Solution steps

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

Manipulating left side

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

Expand

(cos (x) - sin (x))^{2} : cos^{2} (x) - 2 cos (x) sin (x) + sin^{2} (x)

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

Rewrite using trig identities

= 1 - 2 cos (x) sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (α + β) + sin (α - β) = 2 sin (α) cos (β)

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

2 sin (x) cos (x) = sin (2 x)

cos (x) tan^{2} (x) + cos (x) = sec (x)

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