Question

If f(x) = `(1 - sin x + cos x)/(1 + sin x + cos x)`, for x ≠ π is continuous at x = π, then t(π) = ______.

Options

• 1

• - 1

• 0

• 2

Answer 1

If f(x) = `(1 - sin x + cos x)/(1 + sin x + cos x)`, for x ≠ π is continuous at x = π, then t(π) = - 1.

Explanation:

We have,

f(x) = `(1 - sin x + cos x)/(1 + sin x + cos x)`

f(x) = `(1 + cos x - sin x)/(1 + cos x + sin x)`

f(x) = `(2 cos^2  x/2 - 2 sin  x/2 cos  x/2)/(2 cos^2  x/2 + 2 sin  x/2 cos  x/2)`

f(x) = `(2 cos  x/2 (cos  x/2 - sin  x/2))/(2 cos  x/2 (cos  x/2 + sin  x/2))`

f(x) = `(cos  x/2 - sin  x/2)/(cos  x/2 + sin  x/2)`

f(π) = `(cos  pi/2 - sin  pi/2)/(cos  pi/2 + sin  pi/2)`

`= (0 - 1)/(0 + 1)` = - 1