What is expand (asin(t)cos(p)-dsin(p))^2 ?

The solution to expand (asin(t)cos(p)-dsin(p))^2 is d^2sin^2(p)+a^2sin^2(t)cos^2(p)-adsin(t)sin(2p)

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expand (asin(t)cos(p)-dsin(p))^2

expand

(a sin (t) cos (p) - d sin (p))^{2}

d^{2} sin^{2} (p) + a^{2} sin^{2} (t) cos^{2} (p) - a d sin (t) sin (2 p)

Solution steps

(a sin (t) cos (p) - d sin (p))^{2}

Apply Perfect Square Formula:

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

(a sin (t) cos (p) - d sin (p))^{2} = (a sin (t) cos (p))^{2} - 2 a sin (t) cos (p) d sin (p) + (d sin (p))^{2}

= (a sin (t) cos (p))^{2} - 2 a sin (t) cos (p) d sin (p) + (d sin (p))^{2}

Simplify

(a sin (t) cos (p))^{2} - 2 a sin (t) cos (p) d sin (p) + (d sin (p))^{2} : d^{2} sin^{2} (p) + a^{2} sin^{2} (t) cos^{2} (p) - a d sin (t) sin (2 p)

= d^{2} sin^{2} (p) + a^{2} sin^{2} (t) cos^{2} (p) - a d sin (t) sin (2 p)

4 (2 x y + 4 y - 3) d x + (x + 2)^{2} d y

- \frac{6}{( x - 6 ) ^{2}}

\frac{\partial}{\partial u} ((y) (u + v))

\frac{( 0.04 - x ) ( x )}{0.12 - x}

\frac{d}{d y} ((x) (x^{2} + 2 x + 1))

What is expand (asin(t)cos(p)-dsin(p))^2 ?
The solution to expand (asin(t)cos(p)-dsin(p))^2 is d^2sin^2(p)+a^2sin^2(t)cos^2(p)-adsin(t)sin(2p)