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

The solution to expand ((1-cos(2x))/2)^2 is 1/4-(cos(2x))/2+(cos^2(2x))/4

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

expand

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

\frac{1}{4} - \frac{cos ( 2 x )}{2} + \frac{cos ^{2} ( 2 x )}{4}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 1 - cos ( 2 x ) ) ^{2}}{2 ^{2}}

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

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

2^{2} = 4

= \frac{1 - 2 cos ( 2 x ) + cos ^{2} ( 2 x )}{4}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 - 2 cos ( 2 x ) + cos ^{2} ( 2 x )}{4} = \frac{1}{4} - \frac{2 cos ( 2 x )}{4} + \frac{cos ^{2} ( 2 x )}{4}

= \frac{1}{4} - \frac{2 cos ( 2 x )}{4} + \frac{cos ^{2} ( 2 x )}{4}

Cancel

\frac{2 cos ( 2 x )}{4} : \frac{cos ( 2 x )}{2}

= \frac{1}{4} - \frac{cos ( 2 x )}{2} + \frac{cos ^{2} ( 2 x )}{4}

sin (x) cos (x) (tan (x) + csc (x))

cos (y) d x + (2 x \cdot sin (y) - cos^{3} (y)) d y

(1, - 6) y (- 2, - 3)

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

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

What is expand ((1-cos(2x))/2)^2 ?
The solution to expand ((1-cos(2x))/2)^2 is 1/4-(cos(2x))/2+(cos^2(2x))/4