If $117 cos^2 A + 129 sin^2A = 120 $ and $170 cos^2 B + 158sin^2 B = 161 $, then the value of $cosec^2A\,  sec^2B$ is :

16

117cos²A + 129sin²A = 120

117cos²A + 117sin²A + 12sin²A = 120

{ cos²A + sin²A = 1 }

12sin²A = 120 - 117 = 3

sinA = \(\frac{1 }{2}\)

cosecA = 2

Now,

170 cos²B + 158 sin²B = 161

158 cos²B + 12 cos²B + 158 sin²B = 161

12 cos²B = 3

cosB = \(\frac{1 }{2}\)

secB = 2

Now, cosec²A. sec²B

= (2)² . (2)²

= 16