Question

1. If \( \sqrt{ } 5 \sin \theta-\cos \theta=0 \) and \( 0^{\circ}<\theta<90^{\circ} \), find θ.

2. Evaluate \( : \frac{\cos 45^{\circ}}{\sec 30^{\circ}}+\frac{1}{\sec 60^{\circ}} \).

Answer 1

1. \(\sqrt 5 sin \theta - cos \theta = 0\) 

⇒ \(\frac{sin\theta}{cos\theta} = \frac1{\sqrt 5}\)

⇒ \(tan \theta = \frac1{\sqrt5}\)

⇒ \(\theta = tan^{-1}\left(\frac 1{\sqrt 5}\right), 0° < \theta < 90° \) 

\(\therefore \theta = 24 ° \) (approx)  (Using scientific calculator)

2. \(\frac{cos 45°}{sec 30°} + \frac 1{sec 60°}= \frac{\frac 1{\sqrt 2}}{\frac 2{\sqrt 3}} + \frac 12\)

\(= \frac{\sqrt 3}{2\sqrt 2} + \frac 12 = \frac {\sqrt 3 + \sqrt 2}{2\sqrt 2}\)