What is expand sqrt((1-cos(θ))^2+sin^2(θ))dθ ?

The solution to expand sqrt((1-cos(θ))^2+sin^2(θ))dθ is dθsqrt(-2cos(θ)+2)

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expand sqrt((1-cos(θ))^2+sin^2(θ))dθ

expand

(1 - cos (θ))^{2} + sin^{2} (θ) d θ

d θ - 2 cos (θ) + 2

Solution steps

(1 - cos (θ))^{2} + sin^{2} (θ) d θ

(1 - cos (θ))^{2} + sin^{2} (θ) = 1 - 2 cos (θ) + cos^{2} (θ) + sin^{2} (θ)

= d θ cos^{2} (θ) + sin^{2} (θ) - 2 cos (θ) + 1

Use the Pythagorean identity:

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

= 1 - 2 cos (θ) + 1 d θ

Simplify

1 - 2 cos (θ) + 1 : - 2 cos (θ) + 2

= d θ - 2 cos (θ) + 2

\frac{2 x ^{3} - 5 x ^{2} + 4 x}{( x - 1 ) ^{2}}

\frac{x ^{2} + 2}{( x + 2 ) ^{2} ( x + 3 )}

(\frac{1}{3 - y})^{3}

\frac{d ^{2}}{d t ^{2}} ((s) (t^{5} - 10 t^{2}))

\frac{6}{x ( 3 + 2 x )}

What is expand sqrt((1-cos(θ))^2+sin^2(θ))dθ ?
The solution to expand sqrt((1-cos(θ))^2+sin^2(θ))dθ is dθsqrt(-2cos(θ)+2)