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Some Applications Of Trigonometry

Question

Evaluate:
2 tan² 45° + cos² 30° - sin² 60°

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Solution

2 tan² 45° + cos² 30° - sin² 60°

equals space 2 left parenthesis 1 right parenthesis squared plus open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared minus open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared equals space 2 plus 3 over 4 minus 3 over 4 space equals space 2.