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perpendicular/base. Tan(x) depends on the angle x.

Tan(x) = perpendicular/base = y/x

Tan(x) = sin(x) / cos(x)

Cot(x) = 1 / tan(x)

Cot (x) = base/perpendicular = x/y

In a triangle ABC, angleB=90?

Then tanA = BC/AB = √3/1

BC = √3k and AB = k

By Pythagoras theorem we have

AC

AC = √4k

sinA = BC/AC = √3k/2k = √3/2; cosA = AB/AC = k/2k = 1/2;

cosecA = 1/sinA = 2/√3; secA = 1/ cosA = 2 and cotA = 1/tanA = 1/√3

3 tan (x) = 4 ; tan (x) = 4 /3

3 sin(x) + 2 cos(x) 3 sin(x)/cos(x) + 2 cos/cos(x) 3 tan(x) + 2 3 x 4/3 + 2

--------------------- = ----------------------------------- = ------------- = ------------ = 6/2 = 3

3 sin (x) – 2 cos (x) 3 sin(x)/cos(x) – 2 cos(x)/cos(x) 3 tan(x) – 2 3 x 4/3 – 2

Answer : 3