Question : The value of $\cos^{2}30^{\circ}+\sin^{2}60^{\circ}+\tan^{2}45^{\circ}+\sec^{2}60^{\circ}+\cos0^{\circ}$ is:
Option 1: $4\frac{1}{2}$
Option 2: $5\frac{1}{2}$
Option 3: $6\frac{1}{2}$
Option 4: $7\frac{1}{2}$
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Correct Answer: $7\frac{1}{2}$
Solution :
$\cos^{2}30^{\circ}+\sin^{2}60^{\circ}+\tan^{2}45^{\circ}+\sec^{2}60^{\circ}+\cos0^{\circ}$
$=(\frac{\sqrt3}{2})^2 + (\frac{\sqrt3}{2})^2 + 1 + (2)^2 + 1$
$=\frac{3}{4} + \frac{3}{4} + 1 + 4 + 1$
$=\frac{6}{4} + 6$
$ = \frac{3}{2} + 6 $
$= \frac{15}{2}$
$=7\frac{1}{2}$
Hence, the correct answer is $7\frac{1}{2}$.
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