Question

Evaluate (sin 25° / cos 65°) + (tan 20° x tan 70°).

Solution

1. Angles that add up to 90° are complementary, so cos 65° = cos(90° - 25°) = sin 25°.
2. Therefore, sin 25° / cos 65° = 1.
3. Similarly, tan 70° = tan(90° - 20°) = cot 20°, so tan 20° x tan 70° = tan 20° x cot 20° = 1.
4. The value is 1 + 1 = 2.