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

The solution to sin(arccos(sin(x))) is sqrt(cos^2(x))

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simplify sin(arccos(sin(x)))

simplify

sin (arccos (sin (x)))

cos^{2} (x)

Solution steps

sin (arccos (sin (x)))

Use the following identity:

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

= 1 - sin^{2} (x)

Rewrite using trig identities

= cos^{2} (x)

- sin (2 x + \frac{π}{4})

sin (x - \frac{π}{4}) - 1

\frac{1}{cot ( θ ) sin ( - θ )}

- 3 (\frac{3 sin ( - nπ )}{πn})

3 cos (x - \frac{π}{3})

What is sin(arccos(sin(x))) ?
The solution to sin(arccos(sin(x))) is sqrt(cos^2(x))