Question

Evaluate:
cos 30°. cos 45° - sin 30°. sin 45°

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Solution

cos 30°. cos 45° - sin 30°. sin 45°
=

fraction numerator square root of 3 over denominator 2 end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction minus 1 half cross times fraction numerator 1 over denominator square root of 2 end fraction equals space fraction numerator square root of 3 over denominator 2 square root of 2 end fraction minus fraction numerator 1 over denominator 2 square root of 2 end fraction space equals space fraction numerator square root of 3 minus 1 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals space fraction numerator square root of 6 minus square root of 2 over denominator 4 end fraction.

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