Simplify Trig Equation by Hand: (Cos[x]^2) (Tan[x] + Cot[x]) = Sin[x]*Cos^3[x]

[Complexity]

Homework Statement

(Cos[x]^2) (Tan[x] + Cot[x]) Simplify the equation by hand!

Homework Equations

The Attempt at a Solution

cos^2 / (tan + cot)
cos^2 / (sin/cos + cos/sin) * sin*cos/(sin*cos)
sin*cos^3 / (sin^2 + cos^2)
sin*cos^3 / 1
sin(x) * cos^3(x)

this is wrong b/c i divided it...

NVM found the answer:

(cos^2(x))(sin(x)/cos(x) + cos(x)/sin(x))
cos(x)sin(x) + cos^3(x)/sin(x)
cos(x)sin(x) + cos^2(x)cos(x)/sin(x)
cos(x)sin(x) + (1 - sin^2(x))cos(x)/sin(x)
cos(x)sin(x) + (cos(x) - sin^2(x)cos(x))/sin(x)
cos(x)sin(x) + cot(x) - sin(x)cos(x)
cot(x)

 

[Mentallic]

Sorry, it's wrong because you divided what?

$$\frac{cos^2x}{tanx+cotx}\equiv sinx. cos^3x$$

The question says simplify $$cos^2x(tanx+cotx)$$. Was this a typo?

 

[Mentallic]

It's hard to read what you've done... And I can tell you now that it's not equivalent to cot(x).

 

[ocohen]

I get cot(x) as well, though you can skip quite a few steps in the simplification.
Graphing confirms these are equivalent.