(cos 0º + sin 30º + sin 45º) (sin 90º + cos 60º

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

(cos 0º + sin 30º + sin 45º) (sin 90º + cos 60º – cos 45º) = ?

$\frac{5}{6}$

$\frac{5}{8}$

$\frac{3}{5}$

$\frac{7}{4}$

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(cos 0º + sin 30º + sin 45º) (sin 90º + cos 60º – cos 45º)

$= (1 + \frac{1}{2} + \frac{1}{\sqrt{2}}) (1 + \frac{1}{2} - \frac{1}{\sqrt{2}}) = (\frac{3}{2} + \frac{1}{\sqrt{2}}) (\frac{3}{2} - \frac{1}{\sqrt{2}}) = (\frac{9}{4} - \frac{1}{2}) = \frac{7}{4}$