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)

7 cos (8 π t - \frac{π}{2})

cos (3 π + x)

3 cos (nπ)

sec (arctan (\frac{x}{a}))

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

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