1)tan^2x=3 ?

2)tan x sin^2x=tan x ?

3)2cosx sinx - cos x=0

1.

tan^2 x = 3
tanx =±√3 , so x is in all 4 quadrants

x = 60° , 120° , 240° , 300°

2.
tanx sin^2 x = tanx
tanx(sin^2 x -1) = 0
tanx = 0 or sinx = ± 1

if tanx = 0 , x = 0°, 180°, 360°
if sinx= ±1, then x = 90°, 270°

3.
cosx(2sinx - 1) = 0
cosx = 0 or sinx = 1/2

if cosx = 0, then x = 90°, 270°
if sinx = 1/2, then x = 30°, 150°

I assume you know how to convert these to radians if you have to.

1) To find the value of x in the equation tan^2x = 3, we can follow these steps:

Step 1: Start with the given equation, tan^2x = 3.

Step 2: Apply the tangent identity tan^2x = 1 - cos^2x.
This identity states that tan^2x is equal to 1 minus the square of cosine of x.

Step 3: Substitute the equivalence into the equation, we have:
1 - cos^2x = 3.

Step 4: Rearrange the equation to isolate the term with the cosine:
cos^2x = 1 - 3,
cos^2x = -2.

Step 5: Since cosine values range from -1 to 1, a negative value like -2 is not possible. Therefore, there are no real solutions to this equation.

2) To find the value(s) of x in the equation tan x sin^2x = tan x, we can proceed as follows:

Step 1: Start with the given equation, tan x sin^2x = tan x.

Step 2: Divide both sides of the equation by tan x:
sin^2x = 1.

Step 3: Apply the identity sin^2x + cos^2x = 1.
This identity states that the sum of the squares of sine and cosine of x is equal to 1.

Step 4: Rearrange the equation using the identity:
1 - cos^2x = 1.

Step 5: Simplify the equation:
cos^2x = 0.

Step 6: Take the square root of both sides of the equation:
cosx = 0.

Step 7: Determine the values of x where cosine equals zero.
x = π/2 + πn, where n is an integer.

3) To solve the equation 2cosx sinx - cos x = 0, we can follow these steps:

Step 1: Start with the given equation, 2cosx sinx - cosx = 0.

Step 2: Factor out cosx from the left side of the equation:
cosx(2sinx - 1) = 0.

Step 3: Set each factor equal to zero and solve for x:
cosx = 0,
x = π/2 + πn, where n is an integer.

2sinx - 1 = 0,
sinx = 1/2,
x = π/6 + 2πn or x = 5π/6 + 2πn, where n is an integer.

Thus, the solutions to the equation 2cosx sinx - cosx = 0 are x = π/6 + 2πn, x = 5π/6 + 2πn, and x = π/2 + πn, where n is an integer.