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Question Number 47836 by Aknabob1 last updated on 15/Nov/18

$$prove{cosec}^2\theta -cot\theta cosec\theta =1$$

Answered by $@ty@m last updated on 15/Nov/18

$$LHS={cosec}^2\theta -cot\theta cosec\theta$$$$={cosec}^2\theta -\frac{\cos \theta }{\sin \theta }\times \frac{1}{\sin \theta }$$$$=\frac{1}{\sin {}^2\theta }-\frac{\cos \theta }{\sin {}^2\theta }$$$$=\frac{1-\cos \theta }{\sin {}^2\theta }$$$$=\frac{1-\cos \theta }{1-\cos {}^2\theta }$$$$=\frac{1}{1+\cos \theta }$$$$\ne 1$$$$Thequestioniswrong.$$$$Maybetypoerror.$$$$Pl.check$$

Commented by Aknabob1 last updated on 15/Nov/18

$$thanksiappreciate$$

Answered by peter frank last updated on 15/Nov/18

$$\mathrm{cosec}\theta (\mathrm{cosec}\theta -\cot \theta )$$$$\mathrm{cosec}\theta (\frac{1}{\sin \theta }-\frac{\cos \theta }{\sin \theta })$$$$\frac{\mathrm{cosec}\theta }{\sin \theta }(1-\cos \theta )$$$$\frac{1-\cos \theta }{{\sin }^2\theta }=\frac{1-\cos \theta }{1-{\cos }^2\theta }$$$$=\frac{1-\cos \theta }{1+\cos \theta }$$$$\mathrm{hence}{cosec}^2\theta -cot\theta cosec\theta \ne 1$$$$$$

Commented by Aknabob1 last updated on 15/Nov/18

$$thanksiappreciate$$

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