Question 132

The value of $$\theta$$, which satisfies the equation $$\surd3 tan \theta$$ + 3 = 3 secθ, 0° ≤ θ < 90° is

Solution

Given that $$\surd3 tan \theta$$ + 3 = 3 secθ

Using 1) $$\frac{sin \theta }{cos \theta}$$ = $$tan \theta$$

and 2) $$\frac{1}{cos \theta}$$ = $$sec \theta$$

$$\surd3 tan \theta$$ + 3 = 3 secθ

$$\surd3 \frac{sin \theta}{cos \theta}$$ + 3 = 3 $$\frac{1}{cos \theta}$$

$$\surd3 sin \theta + 3 cos \theta$$ = 3

$$\theta$$ = 0 or 60

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