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

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

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Simplify (sinΒ² π + cosΒ² π)/(cscΒ² π β cotΒ² π).

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### Video Transcript

Simplify sin squared π plus cos squared π divided by csc squared π minus cot squared π.

There are a few trig identities that will help us simplify this expression. We know that sin squared π plus cos squared π is equal to one. So we can actually replace the numerator with one.

And now looking at the denominator, we have csc squared π and cot squared π, csc squared π is equal to cot squared π plus one. So we can replace csc squared π with this. So now we need to add to the bottom the minus cot squared π.

So now we have one divided by cot squared π plus one minus cot squared π. So the cot squared πs cancel, and we are left with one over one. And one divided by one is one.

So it simplifies to be one.

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