Question Video: Using the Pythagorean Identities to Simplify a Trigonometric Expression | Nagwa Question Video: Using the Pythagorean Identities to Simplify a Trigonometric Expression | Nagwa

# Question Video: Using the Pythagorean Identities to Simplify a Trigonometric Expression Mathematics • First Year of Secondary School

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Simplify 31 sinΒ² π + 26 cosΒ² π.

01:50

### Video Transcript

Simplify 31 sin squared π plus 26 cos squared π.

In this question, we are asked to simplify a trigonometric expression. This means we need to determine which trigonometric identities to apply to simplify the given expression. We can do this by first considering the given expression. We see that it involves a sum of sine squared and cosine squared functions.

There are multiple different identities we could use to rewrite this expression. For example, we could try the double angle or angle sum or difference identities. However, when dealing with expressions involving the sum of the square of both the sine and cosine functions, we can easily simplify by using the Pythagorean identity. This tells us that for any angle π₯, the sum of the squares of the sin of π₯ and the cos of π₯ is equal to one.

We can use this identity to simplify the expression. First, we will rewrite the expression to apply this identity. We can split 31 sin squared of π into five sin squared of π plus 26 sin squared π. We can then take out a factor of 26 from the final two terms to obtain the following expression. We can now simplify the expression by applying the Pythagorean identity to get five sin squared π plus 26 times one. We can now reorder these terms and evaluate to find that 31 sin squared π plus 26 cos squared π simplifies to give 26 plus five sin squared π.

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