Question

prove the identity: 1 + cos 2(x)/ sin 2(x) = cot(x)

Answer 1

Please help me! :)

Answer 2

first use double angle identities
\[\sin 2x = 2 \sin x \cos x\]
\[\cos 2x = \cos^2 x - \sin^2 x\]

\[\rightarrow \frac{1+ \cos^2 x -\sin^2 x}{2 \sin x \cos x}\]
From pythagorean identity
\[\cos^2 x = 1-\sin^2 x\]
\[\rightarrow \frac{2 \cos^2 x}{2 \sin x \cos x}\]
i think you can simplify it from here

Answer 3

I really appreciate this, however do you mind finishing the problem out? I don't understand how you will get cot(x) from this?

Answer 4

Factor out 2cos(x).

Answer 5

what cancels?

Answer 6

so are you left with cos/2sinx ?

Answer 7

wait i meant cos/sinx

Answer 8

ooohh I think I get it and cot x = cos x/ sin x, right!!!???

Answer 9

Yes!

Answer 10

yes correct :)

always keep a trig reference chart around to help with identities and what cot is

Answer 11

Whoo hoo! :)

Answer 12

ok - thanks guys!

Answer 13

I do have one more question.... can you help?

Answer 14

if log(subscript a) x=7, what is the value of log(subscript a) (a/x^2) ?

Answer 15

-13