Evaluate the following: 5 ^260^ +4 ^230^ - ^245^ ^230^ + ^230^ - Vidyadip

Question

Evaluate the following:
$\frac{5\cos^260^\circ+4\sec^230^\circ-\tan^245^\circ}{\sin^230^\circ+\cos^230^\circ}$

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Answer

$\frac{5\cos^260^\circ+4\sec^230^\circ-\tan^245^\circ}{\sin^230^\circ+\cos^230^\circ}$
$=\frac{5\big(\frac12\big)^2+4\big(\frac{2}{\sqrt{3}}\big)^2-(1)^2}{\big(\frac12\big)^2+\Big(\frac{\sqrt{3}}{2}\Big)^2}$
$=\frac{\Big(\frac54+\frac{4+4}{3}-1\Big)}{\Big(\frac14+\frac34\Big)}$
$=\frac{\Big(\frac{5}{4}+\frac{16}{3}-\frac{1}{1}\Big)}{\big(\frac44\big)}$
$=\frac{\big(\frac{15+64-12}{12}\big)}{\big(\frac44\big)}$
$=\frac{\big(\frac{67}{12}\big)}{(1)}$
$=\frac{67}{12}$

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