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)

2 (u^{2} + v^{2}) 2 u^{2} + 2 v^{2} + 4

\frac{42 e ^{x} ( - 7 e ^{x} + 6 )}{( 7 e ^{x} + 6 ) ^{3}}

\frac{8}{( x + 4 ) ^{2}}

x δ (x - 2)

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)