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

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Answer 1 · 2018-04-11T04:01:44

$LHS=cos 255°$

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

$=-cos (75^@)$

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

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

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

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

$=-sqrt6/4+sqrt2/4$

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

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