Simplifying the Expression 1 + cot^2x Using Trigonometric Identities

1 + cot^2x =

To simplify the expression 1 + cot^2x, let’s recall the trigonometric identity for cotangent

To simplify the expression 1 + cot^2x, let’s recall the trigonometric identity for cotangent.

The cotangent of an angle x is equal to the reciprocal of the tangent of x:

cot(x) = 1 / tan(x)

Therefore, we can rewrite the expression as:

1 + (1 / tan^2x)

Next, let’s recall the Pythagorean identity for tangent. The Pythagorean identity states that:

1 + tan^2x = sec^2x

Using this identity, we can rewrite the expression as:

1 + (1 / tan^2x) = 1 + cot^2x = sec^2x

Therefore, the simplified expression of 1 + cot^2x is sec^2x.

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