# Question Video: Using the Pythagorean Identities to Evaluate a Trigonometric Function for an Angle Mathematics • 10th Grade

Find the value of secΒ² π given tanΒ² π = 4.

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### Video Transcript

Find the value of sec squared π given tan squared π equals four.

To answer this question, weβre not going to solve the equation tan squared π equals four for π. Instead, weβre going to find a Pythagorean identity that links sec squared π and tan squared π.

To find this identity, weβre going to recall one of the most straightforward trigonometric identities. That is, sin squared π plus cos squared π equals one. We also know that tan π is equal to sin π over cos π. So it follows that tan squared π must also be equal to sin squared π over cos squared π.

And so what weβre going to do is individually divide each of the elements in our first identity by cos squared π. When we do, we can write sin squared π divided by cos squared π is tan squared π. Cos squared π divided by cos squared π is one. And since one over cos π is sec π, we know one over cos squared π is sec squared π.

And so this is the Pythagorean identity weβre going to use. And in fact, we donβt need to derive it each time. We can simply quote that sec squared π is equal to tan squared π plus one. In this question, tan squared π is equal to four. So we can say that sec squared π must be equal to four plus one, which is simply five. And so the value of sec squared π given that tan squared π is equal to four is five.