Does anybody know the steps to finding Tan[x] = 2 Cot[x]?

Answer 1

tan(X) = 2cot(x)

==> tan(x)/cot(x) = 2
==> tan²(x) = 2
==> tan(x) = ±√2
==> x = ±arctan(√2) [this is the exact value)

x ≈ 54.7 (this is the approximate value)

Answer 2

Tan[x] = 2 Cot[x]
Since Cotx = 1/tan x, we get:
tanx = 2/tanx
tan^2 x = 2
tan x = +/- sqrt(2)
So x = 45 degrees or 315 degrees when x=+sqrt(2),
and x= 135 degrees or 225 degrees when x = - sqrt(2)

Answer 3

The cotangent function is just the reciprocal of the tangent function, so let's first simplify this by solving the equation u = 2/u for u. We get u = +/-Sqrt[2]as the answers, which corresponds to tan(x) = +/-Sqrt[2]. You can now use the arctangent function on both sides to find the corresponding values of x.

Answer 4

For making it easy for me to write, i will just use tan to mean
tan(x) and cot to indicate cot(x), etc.That is, i will not mention the arguments of the trig functions.
tan = 2cot
sin/cos = 2 cos/sin
sin² = 2 cos²
sin² / cos² = 2
tan² = 2
tan = ±sqrt(2)

x = arctan(± sqrt(2))
x = ± arctan(sqrt(2))
x = ± 0.95531661812450927816385710251576 radians (approximately)

Answer 5

tg [x] = 2cotg[x]

sen x /cos x = 2 cos x / sen x
sen²x = 2 cos²x
sen²x / cos²x = 2
tg²x = 2
tg x = ±2^¹/2

x = arctg (±2^¹/2)

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Answer 6

cotx=1/tanx. so multiplying the given equation throught by tanx, we have,
(tanx)^2=2
or tanx=+/-sqrt(2)
x=arctan(+/-sqrt(2))
or
x=+/-arctan(sqrt(2))