Question

Need help with the problem I feel like I understand a bit, yet need further help.

Answer 1

Explanation:

Remeber, if we have some fraction,

`(x-y)/(d)`

We can rewrite this as a difference of quotients:

`(x)/(d) -(y)/(d)`

So essentially,

the first step becomes

`(sec(\alpha ))/(sec(\alpha )(tan(\alpha )) -(tan(\alpha ))/(sec(\alpha )(tan(\alpha ))`

Next, remember that we can cancel out common factors in the numerator and denominator.

`(1)/(tan(\alpha )) -(1)/(sec(\alpha ))`

Next in order to match the RHS, we would apply the Reciprocal Identity and get

`cot(a)-cos(\alpha )`

Let me know if you need any further clarification. These types of problems involve math ingenuity so I suggest you to work on recognizing perfect squares, differences of squares, properties of fractions, canceling common factors, etc.