<s>[INST] Trigonometry Table Problem Evaluate the given trigonometric expression:
\[
\frac{5\sin^2 30° + \cos^245° - 4\tan^2 30°}{2\sin30°\cdot\cos 30° + \tan 45°}
\]
 [/INST] HINT: Posted below are some identities/axioms. $$\begin{aligned}\sin 30^{\circ} &=  0.5 \\ \\ \sin 45^{\circ} &= {1 \over \sqrt 2} \\ \\ \cos 30^{\circ} & = {\sqrt3 \over 2} \\ \\ \cos 45^{\circ}& = {1 \over \sqrt 2} \\ \\ \tan \theta &= {\sin \theta \over \cos\theta } \\ \\ \sin^2\theta &= (\sin\theta)^2 \\ \\ \tan^2\theta &= (\tan\theta)^2 \\ \\ \cos^2\theta &= (\cos\theta)^2 \\ \\ n\sin\theta &= n \times \sin \theta \end{aligned} $$
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