How do you evaluate #csc 75#?

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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#.