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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

(cos (θ) - sin (θ))^{2}

Expand

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

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

Rewrite using trig identities

= 1 - 2 cos (θ) sin (θ)

= 1 - 2 sin (θ) cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

(cot (x) + tan (x))^{2} = csc^{2} (x) sec^{2} (x)

(sec (a)) (sin (a)) = tan (a)

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