-
The value of the following is :
(tan 20°)² + (cot 20°)² + 2tan 15°. tan 45°. tan 75° (cosec 70°)² (sec 70°)²
-
- 1
- 4
- 3
- 2
Correct Option: C
tan 20° = tan (90° – 70°) = cot 70°
∴ cot 20° = tan 70°
tan 15° = tan (90° – 75°) = cot 75°
∴ Expression = cot² 70°. sin²70° + tan²70°. cos²70° + 2 cot 75°. tan 75°. tan 45°
| = | . sin² 70° + | sin² 70° | cos² 70° |
cos² 70° + 2 × 1 × 1
= cos²70° + sin²70° + 2 = 1 + 2 = 3
[∵ sinθ . cosecθ = 1 ; cosθ. secθ = 1; tanθ . cotθ = 1]
