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How do you evaluate #cot 195#?

1 Answer

Shwetank Mauria

Jun 29, 2016

#cot195^o=2+sqrt3#

Explanation:

#cot195^o=cot(180^o +15^o)#

= #cot15^o#

Now #cot(x/2)=cos(x/2)/sin(x/2)#

= #(2cos(x/2)xxcos(x/2))/(2cos(x/2)sin(x/2))=(2cos^2(x/2))/sinx#

= #(1+cosx)/sinx=cscx+cotx#

Hence, #cot15^o=csc30^o +cot30^o=2+sqrt3#

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