2022 · Q11
What is the value of the following (2sin 68∘)/(cos22∘) - (2cot 15∘)/(5tan75∘)-(3tan20∘tan40∘tan45∘tan50∘tan70∘)/(5)
Elementary MathematicsTrigonometry
- A-1
- B0
- C1
- D5
Explanation
2sin68°/cos22° = 2 since cos22° = sin68°. Also 2cot15°/(5tan75°) = 2/5 since tan75° = cot15°. Pairing complementary angles, tan20°tan40°tan45°tan50°tan70° = 1, so the third term is 3/5. The total is 2-2/5-3/5 = 1. Hence the keyed option is C.