2020 · Q61
What is (tan x + tan y)(1 – cot x cot y) + (cot x + cot y)(1 – tan x tan y) equal to?
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- D4
Explanation
(tanx + tany)(1 − cotx coty) = (tanx + tany) − (tanx cotx coty + tany cotx coty) = (tanx + tany) − (coty + cotx). Similarly (cotx + coty)(1 − tanx tany) = (cotx + coty) − (tanx + tany). The two bracketed expressions are negatives of each other, so the sum is 0.