What is sin(arccos(x-1)) ?

The solution to sin(arccos(x-1)) is sqrt(-x^2+2x)

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simplify sin(arccos(x-1))

simplify

sin (arccos (x - 1))

- x^{2} + 2 x

Solution steps

sin (arccos (x - 1))

Use the following identity:

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

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

Expand

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

= - x^{2} + 2 x

4 sin (2 x - \frac{π}{4}) + 1

tan (arccos (w))

cos (- n \cdot π)

sec (x - \frac{2 π}{3})

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