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

The solution to (sin(1/2)x-cos(1/2)x)^2 is x^2(-sin(2*1/2)+1)

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simplify (sin(1/2)x-cos(1/2)x)^2

simplify

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

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

Solution steps

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

Factor out common term

x

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

Expand

(sin (\frac{1}{2}) - cos (\frac{1}{2}))^{2} : sin^{2} (\frac{1}{2}) - 2 sin (\frac{1}{2}) cos (\frac{1}{2}) + cos^{2} (\frac{1}{2})

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

Apply the distributive law:

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

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

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

Simplify

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

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

Apply the distributive law:

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

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

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

Apply rule:

a (- b) = - ab

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

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

Apply rule:

a \cdot 1 = a

x^{2} \cdot 1 = x^{2}

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

Factor out common term

x^{2} : x^{2} (- sin (2 \cdot \frac{1}{2}) + 1)

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

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

\frac{d}{d y} ((x) ((1 + 6 x)^{4}))

x^{2} (- a sin (x) + b cos (x))

(x - 8) \cdot (x + 64)

\frac{1}{1 - x} - \frac{1}{x}

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