Solving Trigonometric Equation: Discover the Answer to 1 + cot^2(x) using Trig Identities and Definitions

1 + cot^2x =

csc^2x

There are a couple of ways you could approach this question, but one common method is to use the trigonometric identity:

1 + cot^2(x) = csc^2(x)

Using this identity, we can rewrite the left-hand side of the equation as:

1 + cot^2(x) = csc^2(x)

Therefore, the answer to the equation 1 + cot^2(x) is csc^2(x).

So, the final answer to the given equation is csc^2(x).

Alternatively, we could also use the definition of cotangent and cosecant:

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

csc(x) = 1 / sin(x)

Using these definitions, we can rewrite the left-hand side of the equation as:

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

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

= 1/sin^2(x)

Therefore, the answer to the equation 1 + cot^2(x) is 1/sin^2(x), which can also be written as csc^2(x).

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