What is expand (-asin(z)y+bcos(z))*2rsin(z) ?

The solution to expand (-asin(z)y+bcos(z))*2rsin(z) is brsin(2z)-2ayrsin^2(z)

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expand (-asin(z)y+bcos(z))*2rsin(z)

expand

(- a sin (z) y + b cos (z)) \cdot 2 r sin (z)

b r sin (2 z) - 2 a yr sin^{2} (z)

Solution steps

(- a sin (z) y + b cos (z)) \cdot 2 r sin (z)

= 2 r sin (z) (- a sin (z) y + b cos (z))

Apply the distributive law:

a (b + c) = ab + a c

2 r sin (z) (- a sin (z) y + b cos (z)) = 2 r sin (z) (- a sin (z) y) + 2 r sin (z) b cos (z)

= 2 r sin (z) (- a sin (z) y) + 2 r sin (z) b cos (z)

Simplify

2 r sin (z) (- a sin (z) y) + 2 r sin (z) b cos (z) : b r sin (2 z) - 2 a yr sin^{2} (z)

= b r sin (2 z) - 2 a yr sin^{2} (z)

\frac{e ^{- 2 s} + 1}{( s - 2 ) ( s - 1 )}

(1 - sec (2 x))^{2}

(3 a + b) (3 a - b)

3 r^{4 (5 r^{2} - r + 4)}

\frac{e ^{3 x - 1} ( 3 x ^{2} + 7 x - 3 )}{2 x ^{2} ( x + 3 ) ^{2}}

What is expand (-asin(z)y+bcos(z))*2rsin(z) ?
The solution to expand (-asin(z)y+bcos(z))*2rsin(z) is brsin(2z)-2ayrsin^2(z)