Each expression simplifies to a constant, a single function, o...

Question

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

1/ tan² α + cot α tan α

Accepted Answer

Hello. Today we're going to be simplifying the given trigonometric expression and we'll be writing our answer as a single function. So we are given one divided by cotangent squared of X plus seeking of X multiplied by cosine of X. Let's first take a look at the one divided by to tension squared of X. Now recall that the Pythagorean identity for tangent of X is equal to one divided by cotangent of X. The only issue we have with this identity is that it does not involve a cotangent squared X term. However, we can rewrite this identity slightly by squaring both sides of the Pythagorean identity. Doing so will allow us to rewrite the identity as tangent squared of X equal to one squared which is one divided by cotangent squared of X. We can then use this version of the identity to rewrite one divided by co tangent squared of X as tangent squared of X. Now let's take a look at the C and X term. Recall that the Pythagorean identity for seeking of X is equal to one divided by cosine of X. We can replace seek of X with one divided by cosine of X. And using these two substitutions, we can then rewrite the expression as tangent squared of X plus one divided by cosine of X multiplied by cosine of X. On the right hand side, we can reduce one divided by cosine of X multiply by cosine of X to just one. And this will simplify the expression to be tangent squared of X plus one. Now there's one more identity that we can use. Recall that sin squared of X is equal to tangent squared of X plus one. Using this Pythia identity, we can then rewrite the expression to be second squared of X. And this is going to be the simplest form of the given trigonometric expression. And with that being said, the answer to this problem is going to be B so I hope this video helps you in understanding how to reduce this expression. And I'll go ahead and see you all in the next video.

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
1/ tan² α + cot α tan α

Key Concepts

Trigonometric Identities

Reciprocal Functions

Simplification Techniques

Watch next