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Relation between Trigonometric Ratios

Given that ta...

Question

Given that $t a n θ = \frac{p}{q}$ . Find the value of $\frac{p s i n θ - q c o s θ}{p s i n θ + q c o s θ}$ [3 MARKS]

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Solution

Formula: 1 Mark
Proof: 2 Marks
Given, $t a n θ = \frac{p}{q} \frac{p s i n θ - q c o s θ}{p s i n θ + q c o s θ}$
Dividing the numerator and denominator by $c o s θ$ , we get
$\frac{p s i n θ - q c o s θ}{p s i n θ + q c o s θ} = \frac{p t a n θ - q}{p t a n θ + q} = \frac{p \times \frac{p}{q} - q}{p \times \frac{p}{q} + q} = \frac{\frac{p^{2} - q^{2}}{q}}{\frac{p^{2} + q^{2}}{q}} = \frac{p^{2} - q^{2}}{p^{2} + q^{2}}$

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