Question

Evaluate (5 sin² 30ᴼ + cos² 45ᴼ - 4 tan² 30ᴼ) / ( 2 sin 30ᴼcos 30ᴼ + tan 45ᴼ)

Answer 1

Note that
sin(30°) = 1/2
cos(30°) = √3/2
tan(30°) = 1/√3
cos(45°) = 1/√2
tan(45°) = 1

Therefore
5 sin²(30°) + cos²(45°) - 4 tan²(30°)
= 5*(1/4) + 1/2 - 4*(1/3)
= 5/12
= 0.4167

2 sin(30°) cos(30°) + tan(45°)
= 2(1/2)(√3/2) + 1
= 1.866

$\frac{5sin^{2}(30)^{o}+cos^{2}(30^{o})-4tan^{2}(30^{o})}{2sin(30^{o})cos(30^{o})+tan(45^{o})} = \frac{0.4167}{1.866} =0.2233$

Answer: 0.223