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

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

Popular >

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

prove

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

True

Solution steps

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

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

We showed that the two sides could take the same form

\Rightarrow True

cos (a) = 2 cos^{2} (\frac{a}{2}) - 1

tan^{3} (x) = \frac{sin ^{3} ( x )}{cos ^{3} ( x )}

cos (4 θ) = 1 - 8 sin^{2} (θ) cos^{2} (θ)

tan^{2} (x) - sin^{2} (x) = (tan (x) sin (x))^{2}

cos^{2} (θ) = sin^{2} (θ) - 1

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