Video: Using Pythagorean Identities to Simplify a Trigonometric Expression

Simplify (sinΒ² πœƒ + cosΒ² πœƒ)/(cscΒ² πœƒ βˆ’ cotΒ² πœƒ).

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Video Transcript

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

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

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

So now we have one divided by cot squared πœƒ plus one minus cot squared πœƒ. So the cot squared πœƒs 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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