Someone please help: A student found the exact value of cos 30 degrees using the fact that 30 degrees = 60 degrees minus 30 degrees and got zero. What was his error?

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Someone please help: A student found the exact value of cos 30 degrees using the fact that 30 degrees = 60 degrees minus 30 degrees and got zero. What was his error?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\cos 30=\cos \left( 60-30 \right)=\cos 60\cos 30+\sin 60\sin 30\] the student used wrong formula and written - sign in place of + sign as given above.

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