Curry
  • Curry
cosx/1-tanx + sinx/1-cotx = cosx + sinx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Curry
  • Curry
prove
Curry
  • Curry
and rewrite this in terms of only ssinx and cossx
Curry
  • Curry
co^2(2x-sin2x

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More answers

Curry
  • Curry
cos^2(2x)-sin(2x)
Directrix
  • 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
  • Curry
ye
Directrix
  • Directrix
Let's try some things. What is [(1-tanx)] *[(1-cotx)] =
Curry
  • Curry
um 1-tan-cot+1
Directrix
  • Directrix
So, 2 - tanx - cotx ? Yes?
Curry
  • Curry
ye
Directrix
  • 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
  • Curry
nope
Directrix
  • 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
  • Curry
and quick side question how woulod u solve sin(2x)= 0.5 i got to sinxcosx=0.25
Directrix
  • Directrix
|dw:1332306572063:dw|
Directrix
  • Directrix
Please check that and see if it makes sense.
Curry
  • Curry
ye it makes ense
Directrix
  • 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
  • Curry
ye it is but for some reason i cant simplify that one
Directrix
  • 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
  • Curry
kk
Directrix
  • Directrix
|dw:1332306913326:dw|
Curry
  • Curry
k
Directrix
  • Directrix
|dw:1332307026754:dw|
Curry
  • Curry
k
Curry
  • Curry
u mesed up when u combined the denominators the left ide wa lackiong a negatigve sign so u can combine the fractrion
Curry
  • Curry
u cant combine
Directrix
  • Directrix
Good catch! We should factor.
Directrix
  • Directrix
|dw:1332307426013:dw|
Directrix
  • Directrix
See if you agree.
Curry
  • Curry
what did u factor
Directrix
  • Directrix
1 Attachment
Directrix
  • Directrix
|dw:1332307753002:dw|
Directrix
  • 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
  • Curry
kk i get this one but how do u olve the sin (2x)=0.5
Directrix
  • Directrix
I don't know right out of my head. What's the double angle formula for sine?
Directrix
  • Directrix
Are we supposed to be proving some sort of identity or solving a trigonometric equation over some interval?
Directrix
  • 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
  • Curry
um
Curry
  • Curry
2/4
Curry
  • Curry
its 2sincos= in(2x)
Directrix
  • Directrix
natural log?
Curry
  • Curry
n
Curry
  • Curry
nope
Directrix
  • 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
  • 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
  • Curry
set ofd real
Directrix
  • Directrix
So, we need to write pi/12 in such a way to reflect the infinitely many solutions.
Directrix
  • Directrix
What is the next angle after pi/12 that makes the equation true?
Curry
  • Curry
um anything with a full revolution added to it
Directrix
  • 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
  • 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
  • Directrix
Could we take these: x = π/12 , 5π/12 , 13π/12 , 17π/12 and add multiples of 2 pi to them?
Curry
  • Curry
yep
Curry
  • Curry
hey could u also help me this last problem ssin3x=sinx
Curry
  • Curry
and cos2x=cosx
Directrix
  • Directrix
We do not have an answer to sin(2x) = .5 yet.
Curry
  • Curry
we do thouigh it would be pi/12 + n(pi)
Directrix
  • Directrix
Post each of those other problems in separate threads.
Directrix
  • Directrix
I have an idea on cos(2x) = cos(x)

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