How do you evaluate $cot 195$ ?

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Answer 1 · 2016-06-29T06:54:51

$cot195^o=2+sqrt3$

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

= $cot15^o$

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, $cot15^o=csc30^o +cot30^o=2+sqrt3$

How do you evaluate cot 195cot 195?