Skip navigation

Well, this post was looking for the same thing I was, and nobody seemed to know of any.

The problem with algebra tricks is they’re so context dependent. There’s really only a few things that math books and tests use to make “wicked” problems (list being expanded).

  • 1. Multiplying by the conjugate
  • 2. Factoring using the +C -C trick (complete the square method)

Really the “hard” problems require an algebraic twist, a keen eye, insight – stuff you only get after having practiced with hundreds of problems (and checking the solutions!).

So first,
sosmath: Derivative of sin, cos, tan, csc, sec, cot

Mathworld: Inverse trig functions

trig identities

Now, the rest of this post is just examples of the trick (by name) and a couple of examples that illustrate the trick in action (list being expanded!) (Bear with the non-mathmlness for now!)

1. Multiplying by the conjugate

INTEGRAL( dx / (1 + cos x) )

To solve, you have to multiply the numerator and denominator by ( 1 – cos x ) to get sin2x in the denominator..

2. Factoring using the +C -C trick

INTEGRAL( dx / (x2 + 10x + 30) )

You have to factor (wactor! as my friend used to say) the denominator into ((x+5)2 + 5) by:

x2 + 10x + 25 - 25 + 30
= (x + 5)2 + 5

You know to do +25, -25 BECAUSE half of 10 is 5, and 52 is 25. That method in general is called completing the square and you have to do it all the time.

About these ads

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


Get every new post delivered to your Inbox.

Join 45 other followers

%d bloggers like this: