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Trignometry
4 Jun 2007 22:19:11 IST
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ravi tej
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Joined: 29 May 2007
Posts: 61
4 Jun 2007 22:52:30 IST
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the ans is cot
and the required tan is undefined for sin=1/2 and sin=0
and the required tan is undefined for sin=1/2 and sin=0if u want to know how/?
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4 Jun 2007 23:09:47 IST
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from given eqn , sum of roots 
tan 
= sin 2
tan = sin 2 sum of product of 2 roots at a time =tan1tan2 = cos 2
tan1tan2 = cos 2 tan1 tan2 tan3 = costan1 tan2 tan3 tan4 = -sin
1 tan2 tan3 tan4 = -sintan (1 +2) = (tan1+ tan2 )/(1 - tan1 tan2)
1 +2) = (tan1+ tan2 )/(1 - tan1 tan2)use same formula 2 add tan (3 + 4), again use d same & simplify,
3 + 4), again use d same & simplify, tan { (1 + 2) + (3 + 4) } = (tan - tan1tan2tan3) / (1- tan1tan2tan3tan4 - tan1tan2)
1 + 2) + (3 + 4) } = (tan - tan1tan2tan3) / (1- tan1tan2tan3tan4 - tan1tan2) = (sin2 - cos ) /(1+sin -cos 2)
- cos ) /(1+sin -cos 2) = (2sincos - cos )/(1 +sin -(1 - 2sin2))
cos - cos )/(1 +sin -(1 - 2sin2)) =cot
4 Jun 2007 23:10:39 IST
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yeah sure
if you know this,then it is well & good
else learn it now
tan(x+y+z+..........)=(t1-t3+t5-...........................)/((t0-t2+t4-.............)
where tn is sum of tangents taken n at a timme
for ex. in tan(x+y+z),t2 is tanxtany+tanytanz+tanztanx
and t0 is 1
hence tan (1+2+3+4) is t1-t3/1-t2+t4
1+2+3+4) is t1-t3/1-t2+t4since t1 is sin2x and t2 is cos2x and t3 is cosx and t4
is -sin2x by simple trasformations we get the required result
5 Jun 2007 07:49:49 IST
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Good work irlmarks and lazycol.
Remember :
tan(x1+x2+x3+......) = (T1 - T3 + T5 ........) / (1 - T2 + T4 ......)
where , Tr is the sum of tangents taken r at a time.
So, tan(
1+2+3+4) = (T1 - T3) / (1 - T2 + T4)= (sin2
- cos ) / (1- cos 2 - sin)
tan(1+2+3+4) = (2sincos - cos) / (2sin2 - sin)
tan(1+2+3+4) = (cos)(2sin-1) / (sin)(2sin - 1) = cot
Since we are cancelling 2sin-1 , 2sin-1 
0.
Also for=0 , cot would be undefined.
Remember :
tan(x1+x2+x3+......) = (T1 - T3 + T5 ........) / (1 - T2 + T4 ......)
where , Tr is the sum of tangents taken r at a time.
So, tan(
1+2+3+4) = (T1 - T3) / (1 - T2 + T4)= (sin2 - cos ) / (1- cos 2 - sin)tan(
1+2+3+4) = (2sincos - cos) / (2sin2 - sin)tan(
1+2+3+4) = (cos)(2sin-1) / (sin)(2sin - 1) = cotSince we are cancelling 2sin
-1 , 2sin-1 0.Also for
=0 , cot would be undefined.Free Sign Up!
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