Without using calculator or table of multiplication, show that #cos 255° = (sqrt2-sqrt6)/4#.?

1 Answer
P dilip_k
Apr 11, 2018

#LHS=cos 255° #

#=cos (180^@+75^@)#

#=-cos (75^@)#

#=-cos (45^@+30^@)#

#=-(cos 45^@cos30^@-sin45^@sin30^@)#

#=-(1/sqrt2xxsqrt3/2-1/sqrt2xx1/2)#

#=-1/sqrt2xxsqrt3/2+1/sqrt2xx1/2)#

#=-sqrt6/4+sqrt2/4#

#= (sqrt2-sqrt6)/4=RHS#

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