1 + cot^2x =
csc^2x
There are a couple of ways to approach this problem, but one common method is to use the Pythagorean identity, which states that:
1 + tan^2x = sec^2x
We can rearrange this equation to isolate tan^2x, which gives us:
tan^2x = sec^2x – 1
Now, we can take the reciprocal of both sides to get:
cot^2x = 1 + cosec^2x
Substituting this expression into the original equation, we get:
1 + cot^2x = 1 + (1 + cosec^2x) = 2 + cosec^2x
Therefore, the answer is:
1 + cot^2x = 2 + cosec^2x
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