Question

prove the identity by changing the left side of the equation to show equivalency to the right side. 1+cos 2 theta/sin 2 theta= cot theta

Answer 1

Can you help me with this one too?

Answer 2

That seems to have gotten confused. The actual identity is 1+cot^2(x)=sec^2(x)

Answer 3

hmmm well I'm not sure - that's what the assignment problem says.... I think I have to somehow change 1+cos2theta/sin2theta so that it will equal the other side which is cot theta

Answer 4

We start off with the basic identity sin^2(x)+cos^2(x)=1. Divide by sin^2x to get 1+cos^2(x)/sin^2(x)=1/sec^2(x). This can be turned into 1+cot^2(x)=sec^2(x) using basic trigonometry definitions.

Answer 5

Unless you meant cos(2x)/sin(2x).

Answer 6

ok, no what I typed originally is the problem as I see it on my paper... so you think I can write what you wrote above?

Answer 7

also going back to that other problem you helped me with is the answer 2(2√x) instead of 2(2^1/2) ?

Answer 8

Yes but they mean the same thing.

Answer 9

ok

Answer 10

I have another question if you don't mind :)

Answer 11

prove the identity by changing the left side of the equation to show equivalency to the right side. cos^4 theta - sin^4 theta = 1 - 2 sin^2 theta

Answer 12

Use difference of squares to get (cos^2(x)+sin^2(x))(cos^2(x)-sin^2(x)). This simplifies to cos^2(x)-sin^2(x). Cos^2(x)=1-sin^2(x). Plug this in to get 1-sin^2(x)-sin^2(x). This becomes 1-2sin^2(x), which is the same as the right side.

Answer 13

Oh my gosh you are a life saver! Thank you!

Answer 14

so does theta also equal x, like is it the same thing?

Answer 15

Yes.

Answer 16

ok