Question

(a) If $x cos 60° + y cos 0° + sin 30° - cot 45° = 5$ , then find the value of $x + 2 y$ .

(b) Evaluate: $\frac{t a n ^{2} 60°}{s i n ^{2} 60° + c o s ^{2} 30°}$

Approach

Substitute standard trigonometric values into the expression: $x cos 60° + y cos 0° + sin 30° - cot 45° = x \cdot \frac{1}{2} + y \cdot 1 + \frac{1}{2} - 1 = \frac{x}{2} + y - \frac{1}{2}$ . Simplify to get $x + 2 y = 11$ .

Step-by-step working

1
$x cos 60° + y cos 0° + sin 30° - cot 45° = x \cdot \frac{1}{2} + y \cdot 1 + \frac{1}{2} - 1$
1.5 marks
2
$\frac{x}{2} + y + \frac{1}{2} - 1 = 5 \Rightarrow x + 2 y = 11$
0.5 marks

Concepts used

trigonometric ratiotrigonometric valuesevaluatesimplifyfind value

Approach

Step-by-step working

Concepts used

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