No matter how you found it, the answer would be the same.
You want to know how in terms of sines and cosines you already know and addition formulas.
Let's do it. One way 75°=90°-15°=90°-1/2(30°)
cos(x-y)=cosxcosy+sinxsiny
we need COS15°=cos(1/2(30°))=√((1+cos30°)/2)=√((1+√3/2)/2)
SIN15°=√((1-cos30°)/2)=√((1-√3/2)/2)
NOW cos(90°-15°)=cos90°cos15°+sin90°sin15°
COS75°=0+1*√((1-√3/2)/2)
OR BY KNOWING THAT CO-FUNCTIONS OF COMPLEMENTARY ANGLES ARE EQUAL
COS75°=SIN15° AND USING Sin15°=sin(1/2(30°))=√((1-cos30°)/2)=√((1-√3/2)/2
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