Question

) Consider relation ASG in Figure. Suppose there are two applications that access ASG. The first is issued at five sites and attempts to find the duration of assignment of employees given their numbers. Assume that managers, consultants, engineers, and programmers are located at four different sites. The second application is issued at two sites where the employees with an assignment duration of less than 20 months are managed at one site, whereas those with longer duration are managed at a second site. Derive the primary horizontal fragmentation of ASG using the foregoing information.

Answer 1

Explanation:

LHS = tan4x

= tan(2x + 2x)

use, the formula,

tan(A + B) = (tanA+tanB)/(1-tanA.tanB)

= (tan2x + tan2x)/(1-tan2x.tan2x)

=2tan2x/(1-tan²2x)

again, use the formula,

tan2A = 2tanA/(1-tan²A)

= 2{2tanx/(1-tan²x)}/[1-{2tanx/(1-tan²x)}²]

=4tanx.(1-tan²x)²/(1-tan²x)(1+tan⁴x-2tan²x-4tan²x)

=4tanx.(1-tan²x)/(1-6tan²x+tan⁴x) = RHS