Question

Simplify (sin^2x+sinx-6)/sinx+3

Answer 1

\[\frac{ \sin^2x+sinx-6 }{sinx+3}\]

Answer 2

Let \(\bf sin(x) = u\), then:\[\bf \frac{ u^2+u-6 }{ u+3 }=\frac{\cancel{(u+3)}(u-2)}{\cancel{u+3}}=u-2\]At this point, we can replace u with sin(x) again and we get:\[\bf =u-2=\sin(x)-2\]And we are done with the simplification.

@Jay567

Answer 3

Than you! That's exactly what my book has. Trig proofs are tricky for me!