Can tan theeta be integrated?, Mathematics

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You can integrate tanθ

write tanθ=sinθ/cosθ

so now, integral of tanθ.dθ=integral of sinθ/cosθ.dθ→1

put cosθ=t→2

there fore -sinθ.dθ=dt→3

put 2 and 3 in 1

so,the question becomes integral of tanθ.dθ=integral of -dt/t→4

=-log t +c      →   5                  [reason:dx/x=logx]

put 2 in 5,

 =-log cosθ+C

where C is the integration constant


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3/9/2013 7:36:41 AM

yes you can intergrate tan θ

 tan q = sin q/cos q (1)

let,

y = cos q

so, dy/dq = -sin q

this implies, dq=dy/-sin q  (2)

 

putting values in (1)

∫ 1/-y 

= -log|y|

=-log|cos q|

 so the ∫ tan q = -log|cos q|

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