Explain the importance of factoring and substitution while solving trigonometric equations

It might help to not write
x
for the before and after. That's misleading. What you're doing is writing =3sin()
x
=
3
sin
⁡
(
θ
)
. You're inventing a new variable
θ
that relates to
x
in a way that lets you use trig identities to solve your problem. Plugging in values after your transformation shouldn't give you the same values, since the new integral is in a different variable. We have

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