Without using tables, find the value of \(\frac{\sin 20^\circ}{\cos 70^\circ} + \frac{\cos 25^\circ}{\sin 65^\circ}\)
A
2
B
1
C
o
D
-1
E
-2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Note: sin 20^\circ = cos 70^\circ hence
\(\frac{\sin 20}{\cos 70} = 1\)
Also, cos 65^\circ = sin 25^\circ
\(\frac{\cos 65}{\sin 25} = 1\)
\(\therefore \frac{\sin 20}{\cos 70} + \frac{\cos 65}{\sin 25}\)
= 1 + 1
= 2
Source: Myschool Past Questions Archive (Record #23783)