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

Evaluate $x cos 60° + y cos 0° + sin 30° - cot 45°$ and set it equal to $5$ . Substitute trigonometric values and simplify to get the linear equation $x + 2 y = 11$ .

Step-by-step working

1
Substitute values: $cos 60° = \frac{1}{2}, cos 0° = 1, sin 30° = \frac{1}{2}, cot 45° = 1$
1.5 marks
2
$x (\frac{1}{2}) + y (1) + \frac{1}{2} - 1 = 5 \Rightarrow \frac{x}{2} + y - \frac{1}{2} = 5 \Rightarrow x + 2 y = 11$
0.5 marks

Concepts used

trigonometric ratioevaluatefind valuetrigonometric identitystandard angles

Approach

Step-by-step working

Concepts used

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