Does anyone know how to do this problem?

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Answer 1 · 2018-04-18T23:05:47

#(-sqrt6-sqrt2)/4#

I can use the cosine sum or difference identities

Given #cos(195^@)=cos(225^@-30^@)#

Cosine difference identity: #cos(a-b)=cosacosb+sinasinb#

#cos(225^@-30^@)=cos225^@cos30^@+sin225^@sin30^@#

#cos(225^@-30^@)=(-sqrt2/2)(sqrt3/2)+(-sqrt2/2)(1/2)#

#cos(225^@-30^@)=(-sqrt6/4)+(-sqrt2/4)#

#cos(225^@-30^@)=(-sqrt6-sqrt2)/4#