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Trig Question

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I have a question:

if x = 2sin(x), then find the correct expression for cos.

Currently I have the answer like this: √(1-4sin^2(x)), how could I simplify it further?

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If x = 2 sin(x), then sin (x) = x/2. That means in a right triangle, opposite is x and hypotenuse (diagonal) is 2, That makes the third side ±sqrt (4 - x2) and so

cos (x) = ± sqrt (4 - x^2) / 2

Alternatively use sin2(x) + cos2(x) = 1, sin(x) = x/2, cos(x) = ± sqrt (1 - x2 / 4) = ± sqrt (4 - x^2) / 2

Remember to never skip steps and plug in the proper expression. 

Edited by kw0573
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