Question

lim x tends to π÷2 , then what is the value of (tanx + cotx) ÷ ( tanx - cotx)​

Answer 1

(tan(x) + cot(x)) / (tan(x) - cot(x)) = (tan²(x) + 1) / (tan²(x) - 1)

… = (sin²(x) + cos²(x)) / (sin²(x) - cos²(x))

… = -1/cos(2x)

Then as x approaches π/2, the limit is -1/cos(2•π/2) = -sec(π) = 1.