2x+3 + 3x-4 + 2x+3 + 3x-4 = 78
10x -2 = 78
10x = 80
x=8
deck is 2(8)+3 by 3(8)-4, or 19 by 20
1/sin^2x-1/tan^2x=
1/sin^2x-1/ (sin^2x/cos^2x)<<sin tan= sin/cos>>
= 1/sin^2x- cos^2x / sin^2x
= (1- cos^2x) / sin^2x <<combining into a single fraction>>
sin^2 x / sin^2x <<since 1- cos^2 x sin^2 x
=1
this simplifies to 1.
The shortest value has to be greater than 6 and less than 22 in order for 22 to be one of the 2 longer sides.
