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Question Number 19809 by CheaV last updated on 16/Aug/17

$$\mathrm{If}\sin \theta +\mathrm{cosec}\theta =2,\mathrm{then}{\sin }^2\theta +{\mathrm{cosec}}^2\theta$$$$\mathrm{is}\mathrm{equal}\mathrm{to}$$

Answered by ajfour last updated on 16/Aug/17

$${(\sin \theta +\mathrm{cosec}\theta )}^2=\sin {}^2\theta +\mathrm{cosec}{}^2\theta +2$$$$\Rightarrow 4=\sin {}^2\theta +\mathrm{cosec}{}^2\theta +2$$$$\Rightarrow \sin {}^2\theta +\mathrm{cosec}{}^2\theta =2.$$

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