Trignometric Limits

Question

What is the limit of (cos^2 (x))/(1+cos2x)(2+cos2x) as x approaches pi/2

Answer 1

cos(2x) = 2cos²x - 1

So, 1 + cos(2x) = 2cos²x

The given limit is equivalent to lim_x→π/2 [ (1/2)(1 + cos(2x)) / ((1 + cos(2x))(2 + cos(2x)) ]

= (1/2) lim_x→π/2 [1 / (2 + cos(2x))] = 1/2 [ 1 / (2 + cosπ)] = 1/2

Answer 2

Here you go!! Please contact me if you have further questions! Godbless.