Proving a Trigonometric Identity

Hi Pushpa, let's solve this trigonometric identity together. We want to prove that the left-hand side expression equals two times cotangent squared of theta.

Let's start by expanding the numerator using the square of a sum formula. This gives us sine squared theta plus cosine squared theta plus two sine theta cosine theta.

Recall the fundamental identity that sine squared theta plus cosine squared theta equals one. We can replace that sum in our numerator.

Now, observe that the positive one and negative one in the numerator cancel each other out perfectly.

Now, let's look at the denominator. We can express tangent as sine theta divided by cosine theta.

Next, let's factor out sine theta from both terms in the denominator to simplify things.

Notice that we have a sine theta in both the numerator and the denominator. We can divide those out.