2023 · Q51
What is the value of (cos²32∘+cos²58∘)/(sec²50∘-cot²40∘) + 4 tan 13° tan 37° tan 53° tan 77°?
Elementary MathematicsTrigonometry
- A2
- B3
- C4
- D5
Explanation
Since cos58° = sin32°, the numerator is cos²32° + sin²32° = 1. Since cot40° = tan50°, the denominator is sec²50° − tan²50° = 1. The first term is 1/1 = 1, and 4tan13°tan77°tan37°tan53° = 4(tan13°cot13°)(tan37°cot37°) = 4. The total is 1 + 4 = 5 (D).