Answer:
a² - b² = 1
Step-by-step explanation:
The given parameters are;
sec 50° = a
cot 40° = b
We note that sec(θ) = 1/cos(θ) and cot(θ) = 1/tan(θ)
a² - b² = sec²50° - cot²40°
Given that sec(90 - θ) = cosec(θ) where; cosec(θ) = 1/sin(θ), we have;
sec²50° - cot²40° = sec²(90° - 50°) - cot²40° = sec²(40°) - cot²40°
sec²(40°) - cot²40° = cosec²(40°) - cot²40°
Also we have;
cosoc²(θ) = 1 + cot²(θ)
Therefore, we have;
cosoc²(40°) - cot²40° = 1 + cot²(40°) - cot²40° = 1
Therefore, where sec(50°) = a and cot(40°) = b, the value of a² - b² is 1.
