Question : Find the value of $\frac{\cos 65^{\circ}}{\sin 25^{\circ}}+\frac{5 \sin 19^{\circ}}{\cos 71^{\circ}}-\frac{3 \cos 28^{\circ}}{\sin 62^{\circ}}$.
Option 1: 2
Option 2: 0
Option 3: 1
Option 4: 3
Correct Answer: 3
Solution :
Given: $\frac{\cos 65^{\circ}}{\sin 25^{\circ}}+\frac{5 \sin 19^{\circ}}{\cos 71^{\circ}}-\frac{3 \cos 28^{\circ}}{\sin 62^{\circ}}$
= $\frac{\cos 65^{\circ}}{\sin (90^\circ-65^{\circ})}+\frac{5 \sin (90^\circ-71^{\circ})}{\cos 71^{\circ}}-\frac{3 \cos 28^{\circ}}{\sin (90^\circ-28^{\circ})}$
= $\frac{\cos 65^{\circ}}{\cos 65^{\circ}}+\frac{5 \cos 71^{\circ}}{\cos 71^{\circ}}-\frac{3 \cos 28^{\circ}}{\cos 28^{\circ}}$
= $1 + 5 - 3$
= $3$
Hence, the correct answer is 3.
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