trig
posted by bhavya .
cos@4SIN@=1 then sin@+4cos@=

From the first:
cosØ  1 = 4sinØ
square both sides
cos^2 Ø  2cosØ + 1 = 16sin^2 Ø
cos^2 Ø  2cosØ + 1 = 16(1  cos^2 Ø)
17cos^2 Ø  2cosØ  15 = 0
(17cosØ + 15)(cosØ  1)
cosØ = 15/17 or cosØ = 1
case1: cosØ = 15/17
then sinØ = 8/17 (in 2nd quad)
then sinØ + 4cosØ = 8/17 + 4(15)/17 = 52/17
or
sinØ = 8/17 (in 3rd quad)
then sinØ + 4cosØ = 8/17 + 4(15/17) = 68/17
Case 2: cosØ = 1
then sinØ = 0
and sinØ + 4cosØ = 0 + 4(1) = 4