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Find the value of cos² 𝑥/5 + sin² 𝑥/5.

Find the value of cos squared 𝑥 over five plus sin squared 𝑥 over five.

To solve this problem, we need to recognize a form. This question fits the form sin squared 𝜃 plus cos squared 𝜃. This is the Pythagorean theorem for sine and cosines. It’s probably one of the most important trig identities because we know that sin squared 𝜃 plus cos squared 𝜃 equals one. And in our problem, our 𝜃 value is 𝑥 over five. We’re taking the sine squared of a value. And we’re adding that to the cosine squared of the same value. And when we do that, it will equal one no matter what 𝑥 is.

Based on this identity, cos squared of 𝑥 over five plus sin squared of 𝑥 over five must equal one.

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