cosx/1-tanx + sinx/1-cotx = cosx + sinx

- Curry

cosx/1-tanx + sinx/1-cotx = cosx + sinx

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- Curry

prove

- Curry

and rewrite this in terms of only ssinx and cossx

- Curry

co^2(2x-sin2x

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## More answers

- Curry

cos^2(2x)-sin(2x)

- Directrix

[cosx/(1-tanx)] +[ sinx/(1-cotx)] = cosx + sinx
Is this the problem? I wanted to be sure which terms are in a denominator.

- Curry

ye

- Directrix

Let's try some things. What is [(1-tanx)] *[(1-cotx)] =

- Curry

um 1-tan-cot+1

- Directrix

So, 2 - tanx - cotx ? Yes?

- Curry

ye

- Directrix

Some people begin these proofs by changing terms to be all sines and cosines. Others look for a way to get a common denominator and hope terms will add out. Do you have a preference for one way or another?

- Curry

nope

- Directrix

I'm going to the DRAW and convert to sines and cosines and see what happens. I need you to check as we go along. This approach may work and may not work in terms of producing what we want but that's the way it goes with trig identities. Looking at what we are trying to show: cosx + sinx on the right side makes me think sines and cosines is the way to go.

- Curry

and quick side question how woulod u solve sin(2x)= 0.5
i got to sinxcosx=0.25

- Directrix

|dw:1332306572063:dw|

- Directrix

Please check that and see if it makes sense.

- Curry

ye it makes ense

- Directrix

I can only do one problem at the time without losing focus. That problem you wrote looks like a double angle problem of some sort.

- Curry

ye it is but for some reason i cant simplify that one

- Directrix

I'm back on the original problem. I'll begin to clear fractions. I hope you looked for errors because if we miss any, it's back to scratch but that's the way math goes.

- Curry

kk

- Directrix

|dw:1332306913326:dw|

- Curry

k

- Directrix

|dw:1332307026754:dw|

- Curry

k

- Curry

u mesed up when u combined the denominators the left ide wa lackiong a negatigve sign so u can combine the fractrion

- Curry

u cant combine

- Directrix

Good catch! We should factor.

- Directrix

|dw:1332307426013:dw|

- Directrix

See if you agree.

- Curry

what did u factor

- Directrix

##### 1 Attachment

- Directrix

|dw:1332307753002:dw|

- Directrix

Look at the .jpg upload and then what I just wrote. The key is factoring -1 from the second denominator so as to get the denominators the same after moving the negative one to the numerator with the sine squared x.

- Curry

kk i get this one but how do u olve the sin (2x)=0.5

- Directrix

I don't know right out of my head. What's the double angle formula for sine?

- Directrix

Are we supposed to be proving some sort of identity or solving a trigonometric equation over some interval?

- Directrix

What is (square root of 2 all over 2)^2 ? I think we're going to have some 45 degree angles or pi/4 here and multiples of those.

- Curry

um

- Curry

2/4

- Curry

its 2sincos= in(2x)

- Directrix

natural log?

- Curry

n

- Curry

nope

- Directrix

Look, the original problem is sin(2x) = 1/2.
So where does sine x = 1/2. Why not just take half of that angle?

- Directrix

sin (pi/6) = 1/2.
2x = pi/6
x = pi/12. There's one angle. Are you solving over restricted interval or over the set of reals?

- Curry

set ofd real

- Directrix

So, we need to write pi/12 in such a way to reflect the infinitely many solutions.

- Directrix

What is the next angle after pi/12 that makes the equation true?

- Curry

um anything with a full revolution added to it

- Directrix

Hint: Look at this set of solutions for a set interval:
sin 2x = 0.5
2x = π/6 , 5π/6 , 13π/6 , 17π/6
x = π/12 , 5π/12 , 13π/12 , 17π/12
(for 0 ≤ x ≤ 2π)

- Directrix

Now, that has to be expanded. It would be cool to think of a way to use n to write the answers in a shorter way.

- Directrix

Could we take these: x = π/12 , 5π/12 , 13π/12 , 17π/12
and add multiples of 2 pi to them?

- Curry

yep

- Curry

hey could u also help me this last problem
ssin3x=sinx

- Curry

and cos2x=cosx

- Directrix

We do not have an answer to sin(2x) = .5 yet.

- Curry

we do thouigh it would be pi/12 + n(pi)

- Directrix

Post each of those other problems in separate threads.

- Directrix

I have an idea on cos(2x) = cos(x)

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