\left(cos\right)^{2} 30 º \left(cos\right)^{2} 45 º + 4 \left(sec\right)^{2} 60 º + \frac{1}{2} \left(cos\right)^{2} 90 º

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

$\cos^{2} 30 º \cos^{2} 45 º + 4 \sec^{2} 60 º + \frac{1}{2} \cos^{2} 90 º - 2 \tan^{2} 60 º = ?$

$\frac{75}{8}$

$\frac{73}{8}$

$\frac{83}{8}$

$\frac{81}{8}$

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$\cos^{2} 30 º \cos^{2} 45 º + 4 \sec^{2} 60 º + \frac{1}{2} \cos^{2} 90 º - 2 \tan^{2} 60 º$

${(\frac{\sqrt{3}}{2})}^{2} \cdot {(\frac{1}{\sqrt{2}})}^{2} + (4 \times 2^{2}) + (\frac{1}{2} \times 0^{2}) - 2 \times {(\sqrt{3})}^{2}$

$= (\frac{3}{4} \times \frac{1}{2}) + 16 + 0 - 6 = \frac{3}{8} + 10 = \frac{83}{8}$