SOLUTION: How do I verify cot x - tan x = 2 cot 2 x? I can get as far as (cos^2 x - sin^2 x)/cos x * sin x. I know I need to use a double angle formula here but I don't know how. Than

Algebra ->  Trigonometry-basics -> SOLUTION: How do I verify cot x - tan x = 2 cot 2 x? I can get as far as (cos^2 x - sin^2 x)/cos x * sin x. I know I need to use a double angle formula here but I don't know how. Than      Log On


   

Question 1114784: How do I verify cot x - tan x = 2 cot 2 x?
I can get as far as (cos^2 x - sin^2 x)/cos x * sin x.
I know I need to use a double angle formula here but I don't know how.
Thanks for your help!
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
Instead of solving problems  (or,  better to say,  in order for solve the problem),
you need to learn basic trigonometry formulas and identities.


See the lesson
    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS
in this site, and also all relevant associated lessons to it.


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cot+%28x%29+-+tan+%28x%29+=+2+cot+%282x%29

first solve cot+%282x%29using a double angle formula:
since cot%28a%29=cos%28a%29%2Fsin%28a%29 where a=2x, we have

cot+%282x%29=+cos%282x%29%2Fsin%282x%29

since cos%282x%29=cos%5E2%28x%29-sin%5E2%28x%29 and sin%282x%29=2sin%28x%29cos%28x%29, we have

cot+%282x%29=+%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%282sin%28x%29cos%28x%29%29



cot+%282x%29=+cos%28x%29%2F%282sin%28x%29%29+-sin%28x%29%2F%282cos%28x%29%29

cot+%282x%29=cot%28x%29%2F2+-+tan%28x%29%2F2

then, go back to cot+%28x%29+-+tan+%28x%29+=+2+cot+%282x%29, plug in cot+%282x%29=cot%28x%29%2F2+-+tan%28x%29%2F2:

cot+%28x%29+-+tan+%28x%29+=+2+%28cot%28x%29%2F2+-+tan%28x%29%2F2%29 ...simplify

cot+%28x%29+-+tan+%28x%29+=+cot%28x%29+-+tan%28x%29 -> we have proved that left side is equal to right side