Question #03596

1 Answer
Jan 18, 2018

#cos75^@=+-1/2sqrt(2-sqrt3)=sin165^@#

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^@#