What is expand (xcos(θ)-ysin(θ))^2 ?

The solution to expand (xcos(θ)-ysin(θ))^2 is x^2cos^2(θ)+y^2sin^2(θ)-xysin(2θ)

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expand (xcos(θ)-ysin(θ))^2

expand

(x cos (θ) - y sin (θ))^{2}

x^{2} cos^{2} (θ) + y^{2} sin^{2} (θ) - x y sin (2 θ)

Solution steps

(x cos (θ) - y sin (θ))^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Simplify

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

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

\frac{\partial}{\partial x} ((z) (x^{2} y + 4 x + 3 y))

\frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )}

(x + 5)^{4}

(x^{2} - \frac{1}{x ^{2}}) (x^{2} + \frac{1}{x ^{2}})

(cos (β) - 1) (sin (β) - 1)

What is expand (xcos(θ)-ysin(θ))^2 ?
The solution to expand (xcos(θ)-ysin(θ))^2 is x^2cos^2(θ)+y^2sin^2(θ)-xysin(2θ)