What number should be subtracted from 

$4(sin^260° + cos^4 30°) - ( tan^2 45° - cot^2 30°) + cos^2 45° - cosec^2 45° + sec^2 60°$ to get 2 ?

7

 we know, sinA = cosB Iff A + B = 90º    

Now,

4 (sin4 60º  + cos4 30º ) - ( tan²45º - cot²30º ) + cos²45º - cosec²45º + sec²60º

= 4 ( (√3/2)4  + (√3/2)⁴ ) - ( 1 - (1/√3)² ) + (1/√2)² - (√2)² + 2²

= 4 ( \(\frac{9}{16}\) + \(\frac{9}{16}\) ) - ( 1 - \(\frac{1}{3}\)) + \(\frac{1}{2}\) - 2 + 4

= 9

ATQ,

Let A is subtracted from 9 to get 2.

9 - A = 2

A = 7