Simplifying the Expression 1+cot^2(x) using Trigonometric Identities

1+cot^2(x)=

In order to simplify the expression 1+cot^2(x), let’s first recall the basic trigonometric identities:

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In order to simplify the expression 1+cot^2(x), let’s first recall the basic trigonometric identities:

1. cot(x) = cos(x)/sin(x)
2. sin^2(x) + cos^2(x) = 1

Now, let’s substitute cot(x) with its equivalent in terms of sin(x) and cos(x):

cot^2(x) = (cos(x)/sin(x))^2 = cos^2(x)/sin^2(x)

Now, let’s substitute cot^2(x) in the original expression:

1 + cot^2(x) = 1 + cos^2(x)/sin^2(x)

To solve this problem, we need to convert the above expression into a single fraction. To do so, we’ll need a common denominator. Since sin^2(x) is already in the denominator, we can rewrite 1 as sin^2(x)/sin^2(x):

1 + cot^2(x) = sin^2(x)/sin^2(x) + cos^2(x)/sin^2(x)

Now, combine the fractions:

= (sin^2(x) + cos^2(x))/sin^2(x)

By using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can simplify the numerator:

= 1/sin^2(x)

Therefore, the simplified form of 1+cot^2(x) is 1/sin^2(x).

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