Question

Find the exact value of cos 210º - cot 210º??

Answer 1

`-(3sqrt3)/2`

Explanation:

`210^@" is in the third quadrant where"`

`cos210^@<0" and "cot210^@>0`

`cos210^@`

`=-cos(210-180)^@`

`=-cos30^@=-sqrt3/2`

`tan210^@=tan(210-180)^@=tan30^@=1/sqrt3`

`rArrcot210^@=1/(tan210^@)=1/(1/sqrt3)=sqrt3`

`"hence"`

`cos210^@-cot210^@`

`=-sqrt3/2-sqrt3=-3/2sqrt3=-(3sqrt3)/2`