## Can tan theeta be integrated?, Mathematics

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Ans)

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|  