## 1 + cot^2x =

### To solve the equation 1 + cot^2x, we need to understand that cotangent is the reciprocal of tangent

To solve the equation 1 + cot^2x, we need to understand that cotangent is the reciprocal of tangent. The trigonometric identity we can use is:

cot^2x = 1 / tan^2x

Substituting this identity into the equation, we have:

1 + 1 / tan^2x

To simplify further, we need to find the common denominator:

1 + tan^2x / tan^2x

Combining the terms, we get:

(tan^2x + 1) / tan^2x

Using another trigonometric identity, which states that tan^2x + 1 = sec^2x:

(sec^2x) / tan^2x

Lastly, using the identity that sec^2x = 1 / cos^2x:

(1 / cos^2x) / (sin^2x / cos^2x)

Simplifying further, we have:

1 / sin^2x

Therefore, the equation 1 + cot^2x simplifies to 1 / sin^2x.

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