How do you simplify the expression #(tant+1)/sect#?

1 Answer
Mrs. R
Mar 6, 2018

#sint+cost#

Explanation:

Starting with the beginning expression, we replace #tant# with #sint/cost# and #sect# with #1/cost#

#(tant+1)/sect# = #(sint/cost+1)/(1/cost)#

Getting a common denominator in the numerator and adding,
#color(white)(aaaaaaaa)#=#(sint/cost+cost/cost)/(1/cost)#

#color(white)(aaaaaaaa)#= #((sint+cost)/cost)/(1/cost)#
Dividing the numerator by the denominator,
#color(white)(aaaaaaaa)#=#(sint+cost)/cost-:(1/cost)#
Changing the divide to a multiply and inverting the fraction,
#color(white)(aaaaaaaa)#=#(sint+cost)/costxx(cost/1)#
We see the #cost# cancels out, leaving the resulting simplified expression.
#color(white)(aaaaaaaa)#=#(sint+cost)/cancel(cost)xx(cancel(cost)/1)#
#color(white)(aaaaaaaa)#=#(sint+cost)#

Related questions
See all questions in Fundamental Identities
Impact of this question
4192 views around the world
You can reuse this answer
Creative Commons License