Question

Question #285a4

Answer 1

One proves that an equation is true for all values of x by using identities and axioms to change only one side until it is identical to the other side.

Explanation:

Given:

`(tan(2a)+cot(3b))/(cot(2a)+tan(3b))=tan(2a)/tan(3b)`

On the left side, write everything as the tangent function:

`(tan(2a)+1/tan(3b))/(1/tan(2a)+tan(3b))=tan(2a)/tan(3b)`

Multiply the left side by 1 in the form of `tan(3b)/tan(3b)`:

`(tan(2a)tan(3b)+1)/(tan(3b)/tan(2a)+tan^2(3b))=tan(2a)/tan(3b)`

Multiply the left side by 1 in the form of `tan(2a)/tan(2a)`:

`(tan^2(2a)tan(3b)+tan(2a))/(tan(3b)+tan(2a)tan^2(3b))=tan(2a)/tan(3b)`

Factor out `tan(2a)/tan(3b)`:

`tan(2a)/tan(3b)(tan(2a)tan(3b)+1)/(1+tan(2a)tan(3b))=tan(2a)/tan(3b)`

The second fraction is 1:

`tan(2a)/tan(3b)=tan(2a)/tan(3b)` Q.E.D.