1) Solve the equation

Question

sinx(sinx+1) = 0

I am having trouble with the first step. Could I do sin x^2 + 1 =0?

Answer 1

Using distributive property of multiplication over addition:
p(p+1)=x²+x
If p=sin(x), then
sin(x)(sin(x)+1)=sin²(x)+sin(x)

However, this particular problem does not require the expression to be expanded.
In fact, if
p(p+1)=0, it means that either p=0, or p+1=0.
Substitute p=sin(x), we get:
sin(x)=0 .......(1) or
sin(x)+1=0.......(2)

Solve for x in each of the two cases. The answer is the union of the two sets of answers.