How to Simplify Trigonometric Functions for Derivatives

[communitycoll]

Homework Statement

Finding the derivative of x^2 sin x tan x.

I need to simplify this:

x^2 sin x sec^2 x + x^2 tan x cos x + 2x sin x tan x

to:

x (x sec(x) tan(x) + sin(x) * (x+2 tan(x)))

Homework Equations

Just what you see above.

The Attempt at a Solution

I can get it simplified to x(sin x(x sec^2 x + 2 tan x) + x tan x cos x).

 

[Bohrok]

I'm not sure why the sinx is factored right after the x on the left
Try expanding some of the trig functions and see if you can simplify things to the final answer.
$$x^2\sin x \sec^2x + x^2\tan x \cos x + 2x\sin x \tan x = x\left(x\sin x\cdot\frac{1}{\cos x\cdot \cos x} + x\cdot\frac{\sin x}{\cos x}\cdot\cos x + 2\sin x \tan x\right)$$

 

[eumyang]

Simplifying an expression the way that Wolfram does it is not necessarily the best way. The simplified answer you give is the same as given by Wolfram, except that the order of terms are different. If you really want to simplify the expression this way...

x² sin x sec² x + x² tan x cos x + 2x sin x tan x

Using trig identities, rewrite the part in red as a product of two trig functions, neither of which are raised to an exponent. Then rewrite the part in blue as a single trig function. The rest is just rearranging terms and factoring out the greatest common factor.

 

[communitycoll]

Okay dokey then. Thanks : D