If-sin-t-cos-t-2-3-then-cosec-t-sec-t-

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

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

Answered by bobhans last updated on 21/Jun/21

\Leftrightarrow 1 + 2 \sin t \cos t = \frac{4}{9}

\Rightarrow 2 \sin t \cos t = - \frac{5}{9}

\Rightarrow \sin t \cos t = - \frac{5}{18}

\Leftrightarrow cosec t + \sec t = \frac{2 / 3}{- 5 / 18}

= - \frac{2}{3} . \frac{18}{5}

= - \frac{12}{5}

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