How do you find the exact value of $cos(120^circ+45^circ)$ ?

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Answer 1 · 2018-04-27T07:30:59

$cos(120^@+45^@)=(-1-sqrt3)/(2sqrt2)=(-sqrt2-sqrt6)/4$

As $cos(A+B)=cosAcosB-sinAsinB$

$cos(120^@+45^@)$

= $cos120^@cos45^@-sin120^@sin45^@$

= $(-1/2)*1/sqrt2-sqrt3/2*1/sqrt2$

= $(-1-sqrt3)/(2sqrt2)$

or $(-1-sqrt3)/(2sqrt2)*sqrt2/sqrt2=(-sqrt2-sqrt6)/4$

How do you find the exact value of cos(120^circ+45^circ)cos(120^circ+45^circ)?