Question

Prove cotx+tanx=sec^2x/tanx

Answer 1

\[cotx+tanx=\frac{ \sec^2x }{ tanx}\]

Answer 2

I tried switching cot to its reciprocal identity but it didn't give me the right answer

Answer 3

ok so I would start with the left side and add those together. change both to their quotient identities and then give them common denominators so you can add them

Answer 4

\[\frac{ \cos^2x+\sin^2x }{ ?sinxcosx }\]

Answer 5

Okay got it, so it becomes \[\frac{ cosx^2 +sinx^2 }{ sinxcosx}\] right?

Answer 6

Yeah just like that haha

Answer 7

so then you leave that there and start working on the right side. change sec^2x to its inverse identity and tanx to its quotient identity and divide

Answer 8

let me know what you get once you do that

Answer 9

OKay so sec^2x/tanx = (1/cos^2x)/(sinx/cosx) . You multiply by the reciprocal to divide the fraction, and that ends up equaling 1/cosxsinx

Answer 10

Which then equals the left side correct? so is that it?

Answer 11

yep!!

Answer 12

Awesome thank you so much!

Answer 13

no prob!