2022 · Q55
What is (sec²α + tanα · tanβ - tan²α)² + (tanα - tanβ)² - sec²α · sec²β equal to?
Elementary MathematicsTrigonometry
- A-1
- B0
- C1
- D2
Explanation
Since sec²α-tan²α = 1, the first bracket is 1+tanαtanβ. Expanding and using sec²αsec²β = (1+tan²α)(1+tan²β), every term cancels leaving 0. Hence the keyed option is B.