According to the Pythagorean theorem in a right angle
triangle:
(sin x)^2 + (cos x)^2 =
1
If we'll divide the expression by (cos x)^2, we'll
get:
(sin x)^2/(cos x)^2 + 1 = 1/(cos
x)^2
(tan x)^2 = 1/(cos x)^2 -
1
By definition, the trigonometric function tangent is a
ratio between the opposite cathetus and the adjacent
cathetus.
2sinx - 5cosx =
0
2sin x = 5cos x
If we divide
the entire expression by 5 cos x, we'll get:
(2/5) (sin
x/cos x) = 1
We'll substitute the ratio sin x/cos x = tan
x
(2/5)* tan x =
1
tan x =
5/2
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