What is sqrt(x^2-(xsin(x))^2) ?

The solution to sqrt(x^2-(xsin(x))^2) is xcos(x)

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simplify sqrt(x^2-(xsin(x))^2)

simplify

x^{2} - (x sin (x))^{2}

x cos (x)

Solution steps

x^{2} - (x sin (x))^{2}

Apply exponent rule:

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

= x^{2} - x^{2} sin^{2} (x)

Factor out common term

x^{2}

= x^{2} (1 - sin^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply radical rule:

assuming

a \geq 0

x^{2} = x

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

Use the Pythagorean identity:

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

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

= x cos^{2} (x)

cos^{2} (x) = cos (x)

= x cos (x)

5 sin (3 x - π)

cos (x + \frac{π}{2}) - cos (x)

sin (- x^{3})

sin (π - 2 arcsin (\frac{1}{x}))

sin (\frac{arccos ( - x )}{2} + πn)

What is sqrt(x^2-(xsin(x))^2) ?
The solution to sqrt(x^2-(xsin(x))^2) is xcos(x)