Question

Evaluate:
$\frac{cos 45°}{sec 30° + cosec 30°}$

Approach

Evaluate $\frac{c o s 45°}{s e c 30° + c s c 30°}$ by substituting $cos 45° = \frac{1}{2}$ , $sec 30° = \frac{2}{3}$ , $csc 30° = 2$ . The denominator is $\frac{2}{3} + 2 = \frac{2 + 2 3}{3}$ . Simplify the fraction to get $\frac{3 2 - 6}{8}$ or $\frac{3}{2 2 + 2 6}$ .

Step-by-step working

1
Substitute: $cos 45° = \frac{1}{2}$ , $sec 30° = \frac{2}{3}$ , $csc 30° = 2$ .
0.5 marks
2
Denominator = $\frac{2}{3} + 2 = \frac{2 + 2 3}{3}$ .
1 mark
3
Simplify to $\frac{3}{2 2 + 2 6}$ or rationalize to $\frac{3 2 - 6}{8}$ .
0.5 marks

Concepts used

trigonometrytrigonometric ratiosevaluatecos 45sec 30cosec 30simplify

Approach

Step-by-step working

Concepts used

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