Question

Evaluate the limit `lim_(x rarr pi) sin^2 (4x) / tan^2 (4x)`?

Answer 1

`lim_(x rarr pi) sin^2 (4x) / tan^2 (4x) = 1`

Explanation:

We seek:

`L= lim_(x rarr pi) sin^2 (4x) / tan^2 (4x)`
`\ \ = lim_(x rarr pi) sin^2 (4x) / (sin^2(4x)/cos^2 (4x) )`
`\ \ = lim_(x rarr pi) sin^2 (4x) (cos^2(4x)/sin^2 (4x) )`
`\ \ = lim_(x rarr pi) cos^2(4x)`
`\ \ = cos^2(4pi)`
`\ \ = 1`