Question

5cos² 60 + 4 sec² 30 -tan² 45 / sin² 30 + cos² 30 evaluate the following
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Answer 1

Solution :

$\tt \leadsto \dfrac{5cos^{2} 60 + 4 sec^{2} 30 - tan^{2} 45}{sin^{2}30 + cos^{2} 30}$

$\tt \leadsto \dfrac{5 \times (\dfrac{1}{2})^{2} + 4 \times (\dfrac{2}{\sqrt{3}})^{2} - (1)^{2}}{(\dfrac{1}{2})^{2} + (\dfrac{\sqrt{3}}{2})^{2}}$

$\tt \leadsto \dfrac{5 \times \dfrac{1}{4} + 4 \times \dfrac{4}{3} - 1}{\dfrac{1}{4} + \dfrac{3}{4}}$

$\tt \leadsto \dfrac{\dfrac{5}{4} + \dfrac{16}{3} - 1}{\dfrac{3+1}{4}}$

$\tt \leadsto \dfrac{\dfrac{15+64}{12} - 1}{\dfrac{4}{4}}$

$\tt \leadsto \dfrac{\dfrac{79}{12} - 1}{1}$

$\tt \leadsto \dfrac{79-12}{12}$

$\tt \leadsto \dfrac{67}{12}$