The value of k for which the function f(x) = (4/5)tan(4x)tan(5x), 0 < x < π/2, k+25, x = π/2 is continuous at x = π/2, is

f(x)=(4/5)tan(4x)tan(5x)
lim_{x→π/2}(4/5)tan(4x)tan(5x) = k+25
→lim_{x→π/2}(4/5)tan(4x)cot(5x) = k+25
→(4/5)lim_{x→π/2}(tan(4x).cot(5x)) = k+25
→(4/5)tan(2π)cot(5π/2) = k+25
→(4/5)0 × cos(2π + π/2) = k+25
→(4/5)0 = k+25
→k+25 = 1
→k = -24