Question

sinx + cosx = 1/2 then tanx + cotx

Answer 1

HEY MATE YOUR ANSWER IS HERE....

$\sin \: x + \cos x = \frac{1}{2}$

SQUARING BOTH SIDES..

${ \sin}^{2} x + { \cos}^{2} x \: + 2 \sin \: x \cos \: x \: = \frac{1}{2}$

$2 \sin \: x \cos \: x = \frac{1}{2} - 1$

$2 \sin \: x \cos \: x = - \frac{1}{2}$

$\sin \: x \cos \: x = - \frac{1}{4}$

NOW

$\tan \: x + \cot \: x$

$\frac{ { \sin }^{2} x \: + { \cos }^{2} x}{sinx \: cos \: x}$

$= \frac{1}{sinx \: cosx \: }$

$= \frac{1}{ - \frac{1}{4} }$

SO UR ANSWER IS =

-4

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