# Video: Differentiating Trigonometric Functions Using Pythagorean Identities

If 𝑦 = 5(cos² 2𝑥 + sin² 2𝑥), find d𝑦/d𝑥.

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### Video Transcript

If 𝑦 is equal to five multiplied by cos squared two 𝑥 plus sin squared two 𝑥, find d𝑦 by d𝑥.

In order to work out an expression for d𝑦 by d𝑥, we need to differentiate our equation with respect to 𝑥. At first glance, this appears quite complicated as we need to differentiate cos squared two 𝑥 and also sin squared two 𝑥. However, one of our trigonometric identities states that sin squared 𝑥 plus cos squared 𝑥 is equal to one. This also means that sin squared two 𝑥 plus cos squared two 𝑥 is also equal to one.

Our equation can be simplified to 𝑦 is equal to five multiplied by one. Five multiplied by one is equal to five. Therefore, 𝑦 equals five. We know that differentiating any constant gives us zero. This means that d𝑦 by d𝑥, in this case, equals zero. If 𝑦 is equal to five multiplied by cos squared two 𝑥 plus sin squared two 𝑥, then d𝑦 by d𝑥 equals zero.