If cot of theta is the square root of 3, calculate (sin of theta)(cot of theta) - cos^2 of theta (in exact numbers)

\frac{\sqrt{3} }{2}  - .75

Step-by-step explanation:

cot Θ = Sqrt (3)

SinΘ = 1/2                         CscΘ = 2

CosΘ = Sqrt3 /  2              SecΘ = 2Sqrt3 / 3

TanΘ = Sqrt3 / 3               CotΘ = Sqrt (3)

Cotangent is Adjacent over Opposite

Adjacent = Sqrt 3

Opposite = 1

That means the Hyp = 2 (Pythag Theorem)

Sin Θ * Cot Θ - CosΘ ² =

1/2 * Sqrt 3 - .75 = (Sqrt3 / 2) - .75

Sqrt3 / 2 - .75 is as far as I can get.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

246

step-by-step explanation: