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

1 Answer
Mar 12, 2018

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