If 3 sin A + 4 cos A = 5. prove that : tan A + sec A = 2
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3 sin x + 5 cos x = 5
so 6 sin x/2 cos x/2 = 5 ( 1 - cos x)
so 6 sin x/2 cos x/2 = 10 sin x/2 sin x/2
so sin x/2 = 0 or tan x/2 = 3/5
if sin x/2=0 then 5 sin x - 3 cos x = -3
if tan x/2 = 3/5
then sin x = 15/17 and cos x = 8/17
so 5 sin x - 3 cos x = 3.
so 6 sin x/2 cos x/2 = 5 ( 1 - cos x)
so 6 sin x/2 cos x/2 = 10 sin x/2 sin x/2
so sin x/2 = 0 or tan x/2 = 3/5
if sin x/2=0 then 5 sin x - 3 cos x = -3
if tan x/2 = 3/5
then sin x = 15/17 and cos x = 8/17
so 5 sin x - 3 cos x = 3.
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