Question

If sec a = 5/4, evaluate 1 -tan a/1 + tan a

Answer 1

`(1)/(7)`

Explanation:

Firstly, we can create a right triangle with angle a,

This triangle has a hypotenuse of 5 and an adjacent side of 4.

Using the Pythagorean theorem, we can find that the opposite side is 3

Now that we have the opposite side, we can find the value of tan(a), which is the opposite side over the adjacent side, or
`(3)/(4)`

Once we substitute in our value for tan(a), we can simplify in order to find the value of our equation

`(1-tan(a))/(1+tan(a)) \\\\(1-(3)/(4) )/(1+(3)/(4) ) \\\\((1)/(4) )/((7)/(4) ) \\\\(1)/(4) *(4)/(7) =(1)/(7)`