What is expand (cos(θ)-(e^θ)sin(θ))^2 ?

The solution to expand (cos(θ)-(e^θ)sin(θ))^2 is cos^2(θ)+e^{2θ}sin^2(θ)-e^θsin(2θ)

Popular >

expand (cos(θ)-(e^θ)sin(θ))^2

expand

(cos (θ) - (e^{θ}) sin (θ))^{2}

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

Solution steps

(cos (θ) - (e^{θ}) sin (θ))^{2}

Remove parentheses:

(a) = a

= (cos (θ) - e^{θ} sin (θ))^{2}

Apply Perfect Square Formula:

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

a = cos (θ), b = e^{θ} sin (θ)

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

(e^{θ} sin (θ))^{2} = e^{2 θ} sin^{2} (θ)

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

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

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

(3 x + \frac{π}{3}) \cdot (\frac{3 π}{4} - 2 x)

e^{x^{3}} (3 x^{2} y - x^{2}) d x + e^{x^{3}} d y

\frac{2 ( x + 11 )}{( x - 5 ) ( x + 3 )}

(x + y) l e f t (x - y)

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

What is expand (cos(θ)-(e^θ)sin(θ))^2 ?
The solution to expand (cos(θ)-(e^θ)sin(θ))^2 is cos^2(θ)+e^{2θ}sin^2(θ)-e^θsin(2θ)