tan A + sec A = 3
sin A 1
_____ + _____ = 3
cos A cos A
sin A + 1
_________ = 3
cos A
sin A + 1 = 3 cos A square both sides
sin^2 A + 2sin A + 1 = 9cos^2A
sin^2 A + 2sinA + 1 = 9 ( 1 -sin^2A)
sin^2 A + 2sin A + 1 = 9 - 9sin^2 A simplify as
10sin^2A + 2sin A - 8 = 0 divide through by 2
5sin^2 A + sina - 4 = 0 factor as
(5sinA - 4) ( sin A + 1) = 0
Setting each factor to 0 and solving for A gives us that
sin A = 4/5 or sin A = - 1
If sinA = -1....A = 270°...but the tangent and sec are undefine at the angle
So
sin A =4/5
And cos A = 3/5
Added corrected answer ......
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