Question

Evaluate: √2 tan2 45˚ + cos2 30˚ - sin2 60˚

Answer 1

= root2 × tan^2 45° + cos^2 30° - sin^2 60°

= root2 × (1×1) + (root3/2 × root3/2) - (root3/4 × root3/4)

= (root2 ×1) + 3/4 - 3/4

= root2 × 1 = root2

Ans : root 2

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Answer 2

$\sqrt{2 \: \:} \: . \tan {}^{2} 45 \: + \cos{}^{2}30 \: + \: \sin {}^{2}60 \\ \\ = \sqrt{2 \: \:} .(1) {}^{2} + (\sqrt{3} \div 2 {}^{} ) {}^{2} + (\sqrt{3} \div 2) {}^{2} \\ \\ = \sqrt{2} .(1) + 3 \div 4 + 3 \div 4 \\ \\ = \sqrt{2 } \: + \: 6 \div 4 = 4 \sqrt{2} + 6 \div 4 \\ \\ = 2(2 \sqrt{2} + 3) \div 4 \: = 2 \sqrt{2} + 3 \div 2$