Posted by bhavya on Sunday, August 21, 2011 at 11:25am.
From the first:
cosŲ - 1 = 4sinŲ
square both sides
cos^2 Ų - 2cosŲ + 1 = 16sin^2 Ų
cos^2 Ų - 2cosŲ + 1 = 16(1 - cos^2 Ų)
17cos^2 Ų - 2cosŲ - 15 = 0
(17cosŲ + 15)(cosŲ - 1)
cosŲ = -15/17 or cosŲ = 1
case1: cosŲ = -15/17
then sinŲ = 8/17 (in 2nd quad)
then sinŲ + 4cosŲ = 8/17 + 4(-15)/17 = -52/17
or
sinŲ = -8/17 (in 3rd quad)
then sinŲ + 4cosŲ = -8/17 + 4(-15/17) = -68/17
Case 2: cosŲ = 1
then sinŲ = 0
and sinŲ + 4cosŲ = 0 + 4(1) = 4
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