SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "The expression tan^2(x)/(1+sec(x)) is identical to: a. 1 b. sec(x) - 1 c. tan(x) + sin(x) d. tan^2(x) + sin(x)t

Question 6557: Dear Sir/Madam,
I am confronted with the following problem:
"The expression tan^2(x)/(1+sec(x)) is identical to:
a. 1
b. sec(x) - 1
c. tan(x) + sin(x)
d. tan^2(x) + sin(x)tan(x)
e. csc(x) + sin(x)"
I know that tan^2(x) = sec^2(x) - 1, however, once the equation is (sec^2(x) - 1)/(1 + sec(x)) I don't know how to proceed. Could you help me in solving this question?
Thanks in advance.
Regards,
-Mike
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
(sec^2(x) - 1)/(1 + sec(x))

so, sec^2(x) - 1 can be written as (sec(x)+1)(sec(x)-1): this is just difference of 2 squares. Then you can cancel and you get one of the answers :-)

jon.

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