Find exact value csc 195 degreeSolutionall angles in degrees

Solution

all angles in degrees

csc(195)

=1/sin(195)

=1/sin(150+45)

sin(a+b)=sin(a)cos(b) +cos(a)sin(b)

=1/[sin(150)cos(45)+ cos(150)sin(45)]

=1/[sin(90+60)cos(45)+ cos(90+60)sin(45)]

=1/[cos(60)cos(45)-sin(60)sin(45)]

=1/[(1/2)(1/2)-(3 /2)(1/2)]

=1/[(1-3)/(22)]

=(22)/(1-3)

=(22)(1+3)/[(1-3)*(1+3)]

=(22)(1+3)/(1-3)

=(22)(1+3)/(-2)

=-(2)(1+3)