What is sqrt(1-(cos(x-c))^2) ?

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

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simplify sqrt(1-(cos(x-c))^2)

simplify

1 - (cos (x - c))^{2}

sin (- c + x)

Solution steps

1 - cos^{2} (x - c)

Use the Pythagorean identity:

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

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

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

Apply radical rule:

assuming

a \geq 0

= sin (- c + x)

cos (2 t + \frac{π}{2})

6 cos (2 x + \frac{π}{2})

1 + cot^{2} (θ)

64 - 64 (1 - cos^{2} (x))

cos (n \cdot π + 9 \cdot π)

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