Simplifying the Expression 1 + cot^2x Using Trigonometric Identity csc^2x

1 + cot^2x =

To simplify the expression 1 + cot^2x, let’s start by using a trigonometric identity

To simplify the expression 1 + cot^2x, let’s start by using a trigonometric identity. The trigonometric identity we will use is:

cot^2x + 1 = csc^2x

Rearranging this identity, we can solve for cot^2x:

cot^2x = csc^2x – 1

Now, substituting this into our original expression:

1 + cot^2x = 1 + (csc^2x – 1)

Simplifying further:

1 + cot^2x = 1 + csc^2x – 1

The -1 and +1 in the expression cancel each other out, leaving:

1 + cot^2x = csc^2x

So, the simplified expression is csc^2x.

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