if x = aCosecθ, simplify x/(x^2 - a^2)?
here is what i have so far:
x/(x^2 - a^2)
(aCosecθ)/(a^2 Cosec^2θ)
(aCosecθ)/(a^2 (Cosec^2θ - 1)
(aCosecθ)/(a^2 Cot^2θ)
The final answer is supposed to be (1/a)TanθSecθ
NOTE - Cosec^2θ is Cosec squared theta
Cot^2θ is Cot squared theta
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You can divide top and bottom be a giving cosecθ/(acot^2θ)
and cosecθ=1/sinθ, cotθ=cosθ/sinθ and the fraction F= sinθ/[acos^2θ] after
dividing top and bottom by sinθ.F can be written (1/a)(sinθ/cosθ)(1/cosθ)
= (1/a)tanθsecθ as required.
(X-2)(X+4) You made a splash mistake along with your first bracket, the two do, x(x-2) +4(x-2) or, x(x+4) -2(x+4). this might circulate to, x^2-2x+4x-8 which simplifies all the way down to x^2+2x-8.