Question

Rewrite the expression tanA (tanA + cotA) in terms of a single trigonometric ratio.... I have never added the identities before so I'm not sure what to do next. I have already converted all of the trigonometric functions to sine and cosine functions, but just don't know what to do next :/

Answer 1

Well, well, we meet again ;)
What do you mean by 'single trigonometric ratio'
do you mean just one function (sin, cos, tan, etc) ?

Answer 2

Lol yes indeed (: And yes, it's asking that I simplify this expression into just one function

Answer 3

Ok, is tanA being distributed?

Answer 4

Yes because it's on the outside of the parenthesis, right?

Answer 5

ok, then distribute it ;)

Answer 6

Alright, I know that the first distribution make tanA = tan^2 A, but what about cotA? It's not the same function so do I just place it next to cot A like multiplication?

Answer 7

haha, but what about the *ehem* 'special' relationship between tan and cot... look within yourself :D

Answer 8

Lol special relationship? I never learned about that (:

Answer 9

well, you know that tan = sin/cos, right?
What's cot?

Answer 10

I know they're just the reciprocal of each other

Answer 11

so, if they're reciprocals, then their product is...?

Answer 12

cos/sin

Answer 13

It is...tangent? D: I'm sorry I'm a little lost. Taking a shot in the dark

Answer 14

haha, cos/sin * sin/cos = cos sin/ sin cos which is just...?

Answer 15

cot/tan? :o

Answer 16

remember some of the more fundamental identities:
sin * csc = 1
cos * sec = 1
tan * cot = 1

Answer 17

ohhh, durr. That was right in front of me -_- Lol

Answer 18

so, we've reduced the entire shebang to
tan^2 A + 1
Can you do it from here?

Answer 19

Would it be sec^2 A? (:

Answer 20

That is correct, and that, I believe, is what you were going for?

Answer 21

Yes! Thank you :D

Answer 22

No problem