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Find the value of 5 co $s^{2}$ 60° + 4 se $c^{2}$ 30° - ta $n^{2}$ 45°, then divide by (si $n^{2}$ 30° + co $s^{2}$ 30°).

Class 10Trigonometric Ratios of Standard AnglesTrigonometry

A $\frac{67}{12}$
B $\frac{5}{12}$
C $\frac{11}{3}$
D $\frac{12}{67}$

Step-by-Step Solution

Numerator:

5 (\frac{1}{2})^{2} + 4 (\frac{2}{3})^{2} - 1 = \frac{5}{4} + 4 (\frac{4}{3}) - 1 = \frac{5}{4} + \frac{16}{3} - 1 = \frac{15}{12} + \frac{64}{12} - \frac{12}{12} = \frac{67}{12}

. Denominator = 1. Answer =

\frac{67}{12}

.

Answer: A)

\frac{67}{12}

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