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Given: sin^2x + cos^2x = 1 and triangle XYZ

Prove: a^2 + b^2 = c^2

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The last equation you wrote is only true for a right triangle.

If c is the hypotenuse, a = c sin x and b = c cos x. That comes from the definition of sine and cosine.

Plug that into your
sin^2 x + cos^2 x = 1
formula and see what you get.

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