What is expand (xsin(θ)+ycos(θ))^2 ?

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

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expand (xsin(θ)+ycos(θ))^2

expand

(x sin (θ) + y cos (θ))^{2}

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

Solution steps

(x sin (θ) + y cos (θ))^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(\frac{( - 1 - 41 )}{2})^{4}

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

(62500) π (\frac{2}{3} - \frac{3 3}{8})

(17 - 3) (6 + 2)

\frac{s ^{2} + 12}{( s ^{2} + 9 ) ( x + 2 ) ( x + 1 ) ( x - 1 )}

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