tan^2(x)
Proof:
cos^2(x)+sin^2(x)=1 (Modified Pythagorean theorem)
sin^2(x)=1-cos^2(x) (Property of subtraction)
cos^2(x)-1/cos^2(x)=?
sin^2(x)/cos^2(x)=? (Property of substitution)
sin(x)/cos(x) * sin(x)/cos(x) = tan(x) * tan(x) (Definition of tanget)
= tan^2(x)
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If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
sin squared
(1+cosx)(1-cosx)= 1 +cosx - cosx -cos^2x (where ^2 means squared) = 1-cos^2x = sin^2x (sin squared x)
(1 - cos(2x))/2, where x is the variable. And/Or, 1 - cos(x)^2, where x is the variable.
Sin2(x)/Cos2(x) is an expression, not an equation. Because it is an expression, it cannot be solved. It can be transformed to other, equivalent expressions, but that is as far as you can go. So, Sin2(x)/Cos2(x) = [Sin(x)/Cos(x)]2 = Tan2x or [1/Cos2(x) - 1] or [Sec2(x) - 1]