√3/2cos15°-(1/2)cos75°=

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√3/2cos15°-(1/2)cos75°=
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√3/2cos15°-(1/2)cos75°=
√3/2cos15°-(1/2)cos75°=

√3/2cos15°-(1/2)cos75°=
=√3/2*sin75-1/2*cos75
=sin75cos30-cos75sin30
=sin(75-30)
=sin45
=√2/2