Question

(a) If $sec A = 2$ and $tan B = 3$ , then find the value of $2 sin A cos B$ .

(b) Evaluate: $\frac{4 c o s ^{3} 6 0 ^{\circ} + cosec 3 0 ^{\circ}}{t a n ^{2} 3 0 ^{\circ}}$

Approach

Given $sec A = 2$ and $tan B = 3$ , we find $A = 45°$ and $B = 60°$ . Then $2 sin A cos B = 2 sin 45° cos 60° = 2 \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{2} = \frac{2}{2}$ .

Step-by-step working

1
$sec A = 2 \Rightarrow A = 45°$ ; $tan B = 3 \Rightarrow B = 60°$ .
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2
$2 sin A cos B = 2 sin 45° cos 60° = 2 \times \frac{1}{2} \times \frac{1}{2} = \frac{2}{2}$ .
1 mark

Concepts used

trigonometric ratiossectancosevaluate

Approach

Step-by-step working

Concepts used

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