Question #03596
1 Answer
Jan 18, 2018
Explanation:
#"using "color(blue)"half angle formulae"#
#•color(white)(x)cos(x/2)=+-sqrt((1+cosx)/2)#
#•color(white)(x)sin(x/2)=+-sqrt((1-cosx)/2)#
#rArrcos75^@=+-sqrt((1+cos150^@)/2)#
#color(white)(rArrcos75^@)=+-sqrt((1-cos30^@)/2)#
#color(white)(rArrcos75^@)=+-sqrt((1-sqrt3/2)/2)#
#color(white)(rArrcos75^@)=+-sqrt((2-sqrt3)/4)#
#color(white)(rArrcos75^@)=+-1/2sqrt(2-sqrt3)#
#rArrsin165^@=+-sqrt((1-cos330^@)/2)#
#color(white)(rArrsin165^@)=+-sqrt((1-cos30^@)/2)#
#color(white)(rArrsin165^@)=+-sqrt((1-sqrt3/2)/2)=+-1/2sqrt(2-sqrt3)#
#rArrcos75^@=+-1/2sqrt(2-sqrt3)=sin165^@#