# How do you simplify: cos^2x+cos^2(π/2-x) ?

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[ \cos^2x + \cos^2\left(\frac{\pi}{2} - x\right) ]

Using the trigonometric identity ( \sin^2\theta + \cos^2\theta = 1 ), we can simplify the expression:

[ \cos^2x + \cos^2\left(\frac{\pi}{2} - x\right) = \cos^2x + \sin^2\left(\frac{\pi}{2} - x\right) ]

Recall that ( \sin\left(\frac{\pi}{2} - x\right) = \cos x ), so:

[ \cos^2x + \sin^2\left(\frac{\pi}{2} - x\right) = \cos^2x + \cos^2x ]

Combine like terms:

[ \cos^2x + \cos^2x = 2\cos^2x ]

So, the simplified expression is ( 2\cos^2x ).

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