Question 111

If $$tanθ = \frac{a}{b}$$, then $$\frac{a sin \theta + b cos \theta}{a sin \theta - b cos\theta}$$ is

Solution

To find : $$\frac{a sin \theta + b cos \theta}{a sin \theta - b cos\theta}$$

Dividing numerator and denominator by $$cos \theta$$, we get :

= $$\frac{a tan \theta + b}{a tan \theta - b}$$

Also, it is given that $$tanθ = \frac{a}{b}$$

= $$\frac{a \times \frac{a}{b} + b}{a \times \frac{a}{b} - b}$$

= $$\frac{\frac{a^2 + b^2}{b}}{\frac{a^2 - b^2}{b}}$$

= $$\frac{a^2 + b^2}{a^2 - b^2}$$

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