Question #cdf91

1 Answer
sente
Oct 7, 2016

Using the following:

  • (x+y)(x-y)=x^2-y^2

  • csc(x) = 1/sin(x)

  • csc^2(x) - 1 = cot^2(x)

we have

sin(A)/(csc(A)-1) = (sin(A)(csc(A)+1))/((csc(A)-1)(csc(A)+1))

=(sin(A)csc(A)+sin(A))/(csc^2(A)-1^2)

=(sin(A)*1/sin(A)+sin(A))/(csc^2(A)-1)

=(1+sin(A))/cot^2(A)

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