Question

How do you simplify 6 sin(t) + 7 tan(t)/tan(t)?

Answer 1

I'm assuming there is a parenthesis around the first two terms, see below:

Explanation:

If there isn't a parenthesis around the first two terms then the answer is: `6sint+7` since the `tant` cancels out however, since that is not the case our expression is:

`(6sint+7tant)/tant`

To simplify, split the numerator:

`(6sint)/tant+ (7cancel(tant))/cancel (tant)`

Apply the quotient identity (`tant=sint/cost`) to the expression left:

`(6sint)/(sint/cost)+7`

When diving fractions, flip the second number and multiply:

`6cancel(sint)*cost/cancel(sint)+7`

`6cost+7` final answer