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Question Number 167716 by cortano1 last updated on 23/Mar/22

Answered by mahdipoor last updated on 23/Mar/22

$$\Rightarrow$$$$f^{{}^{\prime }}\left(x\right)=cosx+f^{{}^{\prime }}\left(x\right)(2sinx-{sin}^{2}x)$$$$\Rightarrow f^{{}^{\prime }}\left(x\right)=\frac{cosx}{1+{sin}^{2}x-2sinx}=\frac{cosx}{{(1-sinx)}^2}$$$$\Rightarrow f\left(x\right)=\int \frac{cosx.dx}{{(1-sinx)}^2}=-\int \frac{{(1-sinx)}^{{}^{\prime }}}{{(1-sinx)}^2}=$$$$\frac{1}{(1-sinx)}+C$$

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