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Question Number 144086 by liberty last updated on 21/Jun/21

$$\mathrm{If}\sin \mathrm{t}+\cos \mathrm{t}=\frac{2}{3}\mathrm{then}\mathrm{cosec}\mathrm{t}+\sec \mathrm{t}=?$$

Answered by bobhans last updated on 21/Jun/21

$$\iff 1+2\sin \mathrm{t}\cos \mathrm{t}=\frac{4}{9}$$$$\Rightarrow 2\sin \mathrm{t}\cos \mathrm{t}=-\frac{5}{9}$$$$\Rightarrow \sin \mathrm{t}\cos \mathrm{t}=-\frac{5}{18}$$$$\iff \mathrm{cosec}\mathrm{t}+\sec \mathrm{t}=\frac{2/3}{-5/18}$$$$=-\frac{2}{3}.\frac{18}{5}$$$$=-\frac{12}{5}$$

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