Given-sin-x-cos-x-5-6-Find-the-value-of-1-sin-x-1-cos-x-

Question Number 128998 by bramlexs22 last updated on 12/Jan/21

Given \sin x + \cos x = \frac{5}{6} . Find

the value of \frac{1}{\sin x} + \frac{1}{\cos x} .

Answered by liberty last updated on 12/Jan/21

From condition \sin x + \cos x = \frac{5}{6}

we get 1 + 2 \sin x \cos x = \frac{25}{36}

2 \sin x \cos x = - \frac{11}{36} or \sin x \cos x = - \frac{11}{72}

so \frac{1}{\sin x} + \frac{1}{\cos x} = \frac{\sin x + \cos x}{\sin x \cos x} = \frac{5}{6} \times (- \frac{72}{11})

= - \frac{60}{11}

Answered by MJS_new last updated on 12/Jan/21

s + c = \frac{5}{6}

{(s + c)}^{2} = \frac{25}{36} \Rightarrow s^{2} + c^{2} + 2 s c = \frac{25}{36} \Rightarrow s c = - \frac{11}{72}

\frac{1}{s} + \frac{1}{c} = \frac{s + c}{s c} = \frac{\frac{5}{6}}{- \frac{11}{72}} = - \frac{60}{11}

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