Question

OI
If sec 50° = a and cot 40° = b, find the value of a2 - b2.​

Answer 1

a² - b² = 1

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.