What is expand (1-cos(x))^2csc^2(x) ?

The solution to expand (1-cos(x))^2csc^2(x) is csc^2(x)-2csc^2(x)cos(x)+csc^2(x)cos^2(x)

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expand (1-cos(x))^2csc^2(x)

expand

(1 - cos (x))^{2} csc^{2} (x)

csc^{2} (x) - 2 csc^{2} (x) cos (x) + csc^{2} (x) cos^{2} (x)

Solution steps

(1 - cos (x))^{2} csc^{2} (x)

= csc^{2} (x) (1 - cos (x))^{2}

Expand

(1 - cos (x))^{2} : 1 - 2 cos (x) + cos^{2} (x)

= csc^{2} (x) (1 - 2 cos (x) + cos^{2} (x))

Apply the distributive law:

m (a + b + c) = ma + mb + m c

csc^{2} (x) (1 - 2 cos (x) + cos^{2} (x)) = csc^{2} (x) \cdot 1 + csc^{2} (x) (- 2 cos (x)) + csc^{2} (x) cos^{2} (x)

= csc^{2} (x) \cdot 1 + csc^{2} (x) (- 2 cos (x)) + csc^{2} (x) cos^{2} (x)

Simplify

csc^{2} (x) \cdot 1 + csc^{2} (x) (- 2 cos (x)) + csc^{2} (x) cos^{2} (x) : csc^{2} (x) - 2 csc^{2} (x) cos (x) + csc^{2} (x) cos^{2} (x)

= csc^{2} (x) - 2 csc^{2} (x) cos (x) + csc^{2} (x) cos^{2} (x)

(4, - 6 i) (4 + 6 i)

y^{\frac{1}{4}} (y^{\frac{3}{4}} + y^{\frac{7}{4}})

\frac{2 \cdot ( x + y ) ^{2}}{3}

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

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

What is expand (1-cos(x))^2csc^2(x) ?
The solution to expand (1-cos(x))^2csc^2(x) is csc^2(x)-2csc^2(x)cos(x)+csc^2(x)cos^2(x)