What is expand (cos(θ)(x)+sin(θ)(y))^2 ?

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

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expand (cos(θ)(x)+sin(θ)(y))^2

expand

(cos (θ) (x) + sin (θ) (y))^{2}

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

Solution steps

(cos (θ) (x) + sin (θ) (y))^{2}

Simplify

cos (θ) (x) + sin (θ) (y) : cos (θ) x + sin (θ) y

= (cos (θ) x + sin (θ) y)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

(cos (θ) x)^{2} + 2 cos (θ) x sin (θ) y + (sin (θ) y)^{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{( x - 4 ) n}{( 5 n ) !}

1 + \frac{3 k c}{( s + 3 ) ( s + 1 ) ( 0.5 s + 1 )}

142 + \frac{142 ( x - 142 )}{284}

14 - (27)

\frac{( 3 - x ) ( 10 + 11 x )}{( 3 - 11 x ) ( 8 + 11 x )}

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