What is sqrt(r^2(1-sin^2(2t))) ?

The solution to sqrt(r^2(1-sin^2(2t))) is rcos(2t)

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simplify sqrt(r^2(1-sin^2(2t)))

simplify

r^{2} (1 - sin^{2} (2 t))

r cos (2 t)

Solution steps

r^{2} (1 - sin^{2} (2 t))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= r^{2} - sin^{2} (2 t) + 1

Apply radical rule:

assuming

a \geq 0

r^{2} = r

= r - sin^{2} (2 t) + 1

Use the Pythagorean identity:

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

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

= r cos^{2} (2 t)

cos^{2} (2 t) = cos (2 t)

= r cos (2 t)

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What is sqrt(r^2(1-sin^2(2t))) ?
The solution to sqrt(r^2(1-sin^2(2t))) is rcos(2t)