Without using tables, find the value of: \(\frac{sin 20^\circ}{cos 70^\circ} + \frac{cos 25^\circ}{sin 65^\circ}\)
A
2
B
0
C
1
D
-1
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Since sin x = cos (90 - x) [complementary angles]
.: sin 20 = cos 70
cos 25 = sin 65
. . \(\frac{sin 20}{ cos 70} + \frac{cos 25 }{sin 65}\)
=\(\frac{sin 20 }{ sin 20} + \frac{cos 25 }{cos 25}\) = 1 + 1 = 2
Source: Myschool Past Questions Archive (Record #75914)