How do you evaluate $csc 75$ ?

Question

9004 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-22T03:56:05

$csc75=(sqrt6-sqrt2)~=1.0353$ ..

To find $csc75$ , we first find $sin75 :-$

$sin75=sin(45+30)=sin45cos30+cos45sin30$

$=1/sqrt2*sqrt3/2+1/sqrt2*1/2$

$=(sqrt3+1)/(2sqrt2)$

$=(sqrt6+sqrt2)/4$ .

Hence, $csc75=1/sin75$

$=4/(sqrt6+sqrt2)$

${4(sqrt6-sqrt2)}/{(sqrt6+sqrt2)(sqrt6-sqrt2)}$

$=(sqrt6-sqrt2)$ .

Taking, $sqrt6~=2.4495, and, sqrt2~=1.4142$ , we get,

$csc75~=2.4495-1.4142~=1.0353$ .

How do you evaluate csc 75csc 75?