Question

cos2x/sin2x + sinx/cosx = csc2x

Answer 1

Is that supposed to be cos2x or cos^2 x ?

Answer 2

cos2x

Answer 3

Okay so..

cos2x/sin2x = cot2x = 1/tan2x
sinx/cosx = tan x

Thus by adding them we get the LHS as
1/tan2x + tan x

Understood till here?

Answer 4

yes

Answer 5

Okay do you know what tan2x is?
Use Identity of tan(A+B) :D

Answer 6

2tanx/1-tan^2(x) right?

Answer 7

Awesome.

Now we know

tan2x to be 2tanx/(1-tan^2x)

Thus
1/tan2x + tan x

Equals

(1-tan^2x)/2tanx + tanx

YEAH? :D

Now take LCM as 2tanx
Then write tan in sin/cos form.
And tell me what you get. :D

Answer 8

ahhhh i see!! thank you so much! i was stuck on that second part

Answer 9

Okay so I suppose you got it then. :)

Answer 10

sure did! thank you!

Answer 11

:)