1 + cot^2 x
To simplify the expression 1 + cot^2(x), we need to use the trigonometric identities
To simplify the expression 1 + cot^2(x), we need to use the trigonometric identities.
The identity cot^2(x) = 1 + cosec^2(x) relates cotangent and cosecant. This means that when we have cot^2(x), we can replace it with 1 + cosec^2(x).
Using this identity, we can rewrite the expression as:
1 + cot^2(x) = 1 + (1 + cosec^2(x))
Now, let’s simplify further:
1 + (1 + cosec^2(x)) = 1 + 1 + cosec^2(x) = 2 + cosec^2(x)
Therefore, the simplified expression for 1 + cot^2(x) is 2 + cosec^2(x).
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