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Geometry Level 1

For any value of θ \theta , find the value of sin 2 θ + cos 2 θ \sin^2\theta + \cos^2\theta


The answer is 1.

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2 solutions

( s i n a (sin a s i n b + c o s a sin b + cos a c o s b ) = c o s ( a b ) cos b) = cos (a - b)
( s i n 2 θ + c o s 2 θ ) = c o s ( θ θ ) (sin^{2} \theta + cos^{2} \theta) = cos (\theta - \theta)
= c o s ( 0 ) = 1 = cos (0) = \boxed{1}

Ryan Redz
Jun 3, 2014

pythagorean identity

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