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Evaluate the given trigonometric expression: \[ \frac{5\sin^2 30° + \cos^245° - 4\tan^2 30°}{2\sin30°\cdot\cos 30° + \tan 45°} \]

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What have you tried? –  lhf Sep 19 '12 at 16:38
    
I had inserted the value of given trigonometric values, like sin30=1/√2. And so on. But I am not satisfied with my answer –  Alpha Sep 19 '12 at 16:40
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$\sin 30^{\circ} = 0.5$. –  lhf Sep 19 '12 at 16:42
    
@Alpha: You are almost certainly expected to give an exact expression. It is an exercise in trig functions of "standard" angles. You may be expected to rationalize the denominator. –  André Nicolas Sep 19 '12 at 16:45
    
The entity to be evaluated is an expression, not a problem. –  joriki Sep 19 '12 at 16:46
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1 Answer

up vote 6 down vote accepted

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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