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Question Number 120 by novrya last updated on 25/Jan/15

$$Evaluate\int tan\theta d\theta$$

Answered by ssahoo last updated on 06/Dec/14

$$\int \tan \theta d\theta$$$$=\int \frac{\sin \theta }{\cos \theta }d\theta$$$$\mathrm{substituting}\cos \theta =y$$$$-\sin \theta d\theta =dy$$$$\int \frac{\sin \theta }{\cos \theta }d\theta =\int -\frac{dy}{y}$$$$=-\ln \mid y\mid +C$$$$=-\ln \mid \cos \theta \mid +C$$

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