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

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Solution

cos 45°.cos 30° + sin 45°. sin 30°

equals space fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction cross times 1 half equals fraction numerator square root of 3 over denominator 2 square root of 2 end fraction plus fraction numerator 1 over denominator 2 square root of 2 end fraction equals space fraction numerator square root of 3 plus 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 space equals space fraction numerator square root of 2 left parenthesis square root of 3 plus 1 right parenthesis over denominator 4 end fraction space equals space fraction numerator square root of 6 plus square root of 2 over denominator 4 end fraction.

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