What is the Solution to Simplifying Trig Expressions?

[bobsmith76]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't see how the textbook gets from step 1 to step 2. If anything, the cosines cancel and the answer should be (sine^2)x

 

[Curious3141]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't see how the textbook gets from step 1 to step 2. If anything, the cosines cancel and the answer should be (sine^2)x

One of the best known trigonometric identities is : \cos^2 x + \sin^2 x = 1. To see this, just draw a right angle triangle, with one of the acute angles marked x and the hypotenuse measuring 1 unit. One side (opposite angle x) measures sin x and the other side (adjacent to angle x) measures cos x. You can immediately see the identity with Pythagoras' Theorem.

Remember that \frac{a^2 + b^2}{a^2} \neq b^2. Cancellation doesn't work that way. It is true, however that \frac{a^2b^2}{a^2} = b^2 (when a is nonzero).

 

[bobsmith76]

thanks, trig identities, I forgot about them

 

[solve]

(a-b)/a

You can't cancel a out unless you take the common factor out of parenthesis:

[a(1-b/a)]/a

Now you can cancel a's out and you will be left with 1-b/a

Another example:

(a-ab)/a= [a(1-b)]/a=1-b

To cancel you always have to get the common factor out of parenthesis.

 

[Mark44]

thanks, trig identities, I forgot about them

You pretty much can't simplify trig expressions without having a few identities in mind, so I would advise you to spend some time reviewing them.

I would also advise reviewing basic algebra, particularly fractions and rational expressions, since you seem to have forgotten those concepts, as well. You should wipe the word "cancel" from your mind, since students who are uncertain about what this actually means are prone to making mistakes.