Question

How do I simplify (1 + tan x)^2? Thanks.

Answer 1

You would multiply (1 + tan x)*(1 + tan x) in the same way you would multiply (a+b)*(a+b).

@dbbl21

Answer 2

Thanks for your reply. I did that and simplified it to:

tan^2 x + 2 tan x + 1, then simplified this to:

(sin^2 x / cos^2 x) + 2(sin x / cos x) + 1

I cannot figure out where to go from here.

Answer 3

@dbbl21 There are several ways to write the answer. That is why we need the answer options posted so that we will have an idea of how to proceed.

Answer 4

If I am understanding you correctly there are no answer options, just to simplify.

Answer 5

tan^2 x + 2 tan x + 1 would be where I'd stop, then.

Answer 6

I managed to simplify it down to 2 cos x(sin^2 x) + 2 sin x(cos^2 x). Not sure if it is correct but it is all I can come up with for now. Thanks for your help.

Answer 7

How is this: 2 cos x(sin^2 x) + 2 sin x(cos^2 x) simpler than this: tan^2 x + 2 tan x + 1?
I'll check and see if they are the same.

Answer 8

http://www.wolframalpha.com/input/?i=%281+%2B+tan+x%29%5E2%3D

Answer 9

I would use a trigonometric identity to do this
tan^2x+1=sec^2x
so it would be
(sec^2x)^2
or sec^4x

right?

Answer 10

@GABI_J

I don't think that would work because the posted problem is:

(1 + tan x)² 　≠ (1 + tan²x) in the same way that (a + b)² ≠ (a² + b²)

(1 + tan²x)² does equal sec^4 x for the reasons you gave above.

Lately, I have been wondering if the problem were supposed to be this:

(1 + tan²x) in which case the simplification would be just sec²x x.

Answer 11

yeah, my bad. As you said tan^2 x + 2 tan x + 1
but even on that I would preform one more step
sec^2x+2tanx.

Answer 12

@GABI_J

How do you get from here: tan^2 x + 2 tan x + 1

to here: sec^2x+2tanx ?

Answer 13

b/c
tan^2x=sec^2x-1
so
tan^2x+1=sec^2x