Question

(sin 30°/cos 45°) + (cot 45°/sec 60°) - (sin 60°/tan 45°) - (cos
$\frac{ \sin(30 ) }{ \cos(45) } + \frac{ \cot(45) }{ \sec(60) } - \frac{ \sin(60) }{ \tan(45) } - \frac{ \cos(30) }{ \sin(90) }$
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Answer 1

$\frac{ \sin(30) }{ \cos(45) } + \frac{ \cot(45) }{ \sec(60) } - \frac{ \sin(60) }{ \tan(45) } - \frac{ \cos(30) }{ \sin(90) } \\ = \frac{ \frac{1}{2} }{ \frac{1}{ \sqrt{2} } } + \frac{1}{2} - \frac{ \frac{ \sqrt{3} }{2} }{1} - \frac{ \frac{ \sqrt{3} }{2} }{1} \\ = \frac{1}{2} \times \sqrt{2} + \frac{1}{2} - \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2} \\ = \frac{ \sqrt{2} }{2} + \frac{1}{2} - \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2} \\ = \frac{ \sqrt{2} + 1 - \sqrt{3} - \sqrt{3} }{2} \\ = \frac{1 + \sqrt{2} - 2 \sqrt{3} }{2} \\ if \: required \: further \: simplification \\ = \frac{1 + 1.414 - 2(1.732)}{2} \\ = \frac{2.414 - 3.464}{2} \\ = \frac{ - 1.05}{2} \\ = - 0.525$