anonymous
  • anonymous
how do you simplify 2sin^2(x/2)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
looks pretty simple as is to me :) what are ya going for?
amistre64
  • amistre64
2(1-cos^2(x/2)) = 2 - 2cos^2(x/2) doesnt seem to help..
anonymous
  • anonymous
i got that, but what do I do next? or is that not right

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amistre64
  • amistre64
it all depends on what your definition of "simplified" means... are we wanting only single exponents?
amistre64
  • amistre64
err...exponents of 1?
anonymous
  • anonymous
yes, just one term
amistre64
  • amistre64
one term it already is, but do you mean like sin(x/2) instead of sin^2(x/2)?
anonymous
  • anonymous
yes, i believe so
amistre64
  • amistre64
hmmmm...... we can play around with identites some and see what happens i spose... do you recall the formula for reducing an exponent?
anonymous
  • anonymous
nope, im so hopless haha
amistre64
  • amistre64
cos(2a) = cos^2 - sin^2 cos(2a)= 1 - 2sin^2(2a) cos(t) -1 ------- = sin^2(t) 2 try this one
amistre64
  • amistre64
2(cos(x/2) -1) ------------ = sin^2(x/2) 2
anonymous
  • anonymous
okay, hold on ne second while i work it out
amistre64
  • amistre64
.....2sin^2(x/2)
anonymous
  • anonymous
okay, that worked. i understand that, thanks!
amistre64
  • amistre64
that needs alittle fixing... cos(x)-1 -------- = sin^2(x/2) 2 thats what it should be before you put it in
amistre64
  • amistre64
cos(x) - 1 = 2sin^2(x/2)
anonymous
  • anonymous
ohh, okay, I see it now.
amistre64
  • amistre64
better? :)
anonymous
  • anonymous
yupp, thanks a lot!
amistre64
  • amistre64
to double check, throw in a number and see :)

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