Question 127
The value of $$sin^{2} 30^{\circ} cos^{2} 45^{\circ}$$ + $$5tan^{2} 30^{\circ}$$ + $$\frac{3}{2} sin^{2} 90^{\circ}$$ - $$3 cos^{2} 90^{\circ}$$ is
Solution
Expression : $$sin^{2} 30^{\circ} cos^{2} 45^{\circ}$$ + $$5tan^{2} 30^{\circ}$$ + $$\frac{3}{2} sin^{2} 90^{\circ}$$ - $$3 cos^{2} 90^{\circ}$$
= $$[(\frac{1}{2})^2 * (\frac{1}{\sqrt{2}})^2]$$ + $$5(\frac{1}{\sqrt{3}})^2 + \frac{3}{2}(1^2) - 3(0)^2$$
= $$ (\frac{1}{4}*\frac{1}{2}) + \frac{5}{3} + \frac{3}{2}$$
= $$ \frac{3+40+36}{24}$$
= $$\frac{79}{24} = 3\frac{7}{24}$$
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