Question

Where did I go wrong? Ans from book: http://i.imgur.com/8yA2z.gif My work: http://mathb.in/463

Answer 1

There is a property that says: "If the product of factors is 0 then one of the factors is 0." However there is no property that says "If the product of factors is 1 then one of the factors is 1." And that is where you went wrong.

Answer 2

Could you tie that in to the context of the problem a bit?

Answer 3

You wrote 2sinx2cosx = 1 then you said 2sinx=1 and 2cosx=1

Answer 4

There is not property that says just because you multiply two things and get 1 that one of them would be 1

Answer 5

So I must subtract 1? Then I can set both factors to 0, right?

Answer 6

If you subtract the 1, then you won't have factors. I think I would square both sides and then substitute sin^2x = 1-cos^2x or cos^2x=1-sin^2x

Answer 7

So the main problem was I set it all to 1 and not 0, right?

Answer 8

\[4\sin x \cos x=1\]
\[2(2\sin x \cos x)=1\]
\[2\sin 2x=1\]

Answer 9

This is a better approach. Do you understand so far?

Answer 10

I understand, but I am wanting to know what not to do.

Answer 11

Don't write sinx = 1/2 and cosx = 1/2

Answer 12

That error came from me setting it to 1, right?

Answer 13

yes

Answer 14

Trigonometric identity used to simplify the equation! If you don't recognize this approach, you're pretty much head to the bottle-neck situation !!!