sin(x) = [1 + cot^2(x)]^-0.5
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Cot in trigonometry is the cotangent, which is cosine over sine, or x over y.
No, it is not. To be correct, the expression requires parenthesis, which are missing.
The inverse of sine (sin) is cosecant (csc). The inverse of cosine (cos) is secant (sec). The inverse of tangent (tan) is cotangent (cot).
Cosecant(Csc) = 1 / Sin . Hence its recip[rocal is 'Sin'(Sine). Similarly Secant(Sec) = 1/ Cos . Hence its reciprocal is 'Cos'(Cosine) Cotangent(Cot) = 1 /Tan . Hence its reciprocal is 'Tan'(Tangent).
cot(x) = sqrt[cosec^2(x) - 1]