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Can someone help me w/ these?

  • #1
1)
tan(x)-sin(x)/2tan(x) = sin^2(x/2)
1-sin(x)/2 = sin^2(x/2)

(That's as far as i've gotten on this one...but i don't know if i'm in the right direction or what to do next?)

2)
sin2x = 1 / tanx + cot2x
2sin(x)cos(x) = ''
sin(x) * cos(x) * sin(x) = ''

(The same from #1 applies to this problem)
 

Answers and Replies

  • #2
Pyrrhus
Homework Helper
2,178
1
Assuming you mean:
[tex] \frac{\tan(x)-\sin(x)}{2 \tan(x)} = \sin^{2}(\frac{x}{2}) [/tex]

Let's change everything to cosinus and sinus

[tex] \frac{\frac{\sin(x)}{\cos(x)} - \sin(x)}{\frac{2 \sin(x)} {\cos(x)}} = \sin^{2}(\frac{x}{2}) [/tex]

Simplifying:

[tex] \frac{\frac{\sin(x) - \sin(x) \cos(x)}{\cos(x)}}{\frac{2 \sin(x)} {\cos(x)}} = \sin^{2}(\frac{x}{2}) [/tex]

[tex] \frac{\sin(x) - \sin(x) \cos(x)}{2 \sin(x)} = \sin^{2}(\frac{x}{2}) [/tex]

[tex] \frac{1 - \cos(x)}{2} = \sin^{2}(\frac{x}{2}) [/tex]

Remember [itex] \sin^{2}(\frac{x}{2}) = \frac{1 - \cos(x)}{2} [/itex]

[tex] \frac{1 - \cos(x)}{2} = \sin^{2}(\frac{x}{2}) [/tex]

[tex] \sin^{2}(\frac{x}{2}) = \sin^{2}(\frac{x}{2}) [/tex]

Assuming you mean:
[tex] \sin (2x) = \frac{1}{\tan(x) + \cot(2x)} [/tex]

Working the right to the left

Changing to sinus and cosinus:

[tex] \sin (2x) = \frac{1}{\frac{\sin(x)}{\cos(x)} + \frac{\cos(2x)}{\sin(2x)}} [/tex]

Applying double angle identities

[tex] \sin (2x) = \frac{1}{\frac{\sin(x)}{\cos(x)} + \frac{\cos^2(x) - \sin^2(x)}{2 \sin(x) \cos(x)}} [/tex]

Simplifying:

[tex] \sin (2x) = \frac{1}{\frac{2 \sin^2(x) \cos(x) + \cos^3(x) - \sin^2(x) \cos(x)}{2 \sin(x) \cos^2(x)}} [/tex]

[tex] \sin (2x) = \frac{1}{\frac{\sin^2(x) \cos(x) + \cos^3(x)}{2 \sin(x) \cos^2(x)}} [/tex]

[tex] \sin (2x) = \frac{1}{\frac{\sin^2(x) + \cos^2(x)}{2 \sin(x) \cos(x)}} [/tex]

Remember [itex] \sin^2(x) + \cos^2(x) = 1 [/itex]

[tex] \sin (2x) = \frac{1}{\frac{1}{2 \sin(x) \cos(x)}} [/tex]

Remember [itex] \sin(2x) = 2 \sin(x) \cos(x) [/itex]

[tex] \sin (2x) = 2 \sin(x) \cos(x) [/tex]

[tex] \sin (2x) = \sin (2x) [/tex]
 
Last edited:
  • #3
263
0
damn it... how do u do all these equations on the computer?? i find it hard doin my math on a computer... im more comfortable with a pen and paper... get tired of using the "^",etc

any words of wisdom ?
 
  • #4
Jeez...that was incredible. Thanks a lot...but I don't suppose there was an easier way, was there? haha
 
  • #5
Pyrrhus
Homework Helper
2,178
1
jai6638 said:
damn it... how do u do all these equations on the computer?? i find it hard doin my math on a computer... im more comfortable with a pen and paper... get tired of using the "^",etc

any words of wisdom ?
You get used to imagining it in your head.
 
  • #6
263
0
lol i imagine it in my head too when possible but i just cant get myself to type it all down....Good ol' pen and paper!
 

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