Tính Tag(x) - cot(x) = 1 + 2sin^2x/sinx cosx

To solve the equation Tg(x) - cot(x) = 1 + 2sin^2x/sinxcosx, we can start by simplifying the right side of the equation.

1 + 2sin^2x/sinxcosx = 1 + 2sin^2x/(sinx * cosx)

Using the identity sin^2x + cos^2x = 1, we can rewrite sin^2x as 1 - cos^2x.

1 + 2(1 - cos^2x)/(sinx * cosx)

Now, let's simplify the left side of the equation.

Tg(x) - cot(x)

Using the identity Tg(x) = sinx/cosx and cot(x) = cosx/sinx, we can rewrite the left side of the equation.

sinx/cosx - cosx/sinx

To combine these fractions, we need a common denominator. The common denominator is sinx * cosx.

(sin^2x - cos^2x)/(sinx * cosx)

Using the identity sin^2x + cos^2x = 1, we can simplify the numerator.

(1 - cos^2x - cos^2x)/(sinx * cosx)

(1 - 2cos^2x)/(sinx * cosx)

Now, we have the equation:

(1 - 2cos^2x)/(sinx * cosx) = 1 + 2(1 - cos^2x)/(sinx * cosx)

To simplify further, we can multiply both sides of the equation by sinx * cosx to eliminate the denominators.

1 - 2cos^2x = sinx * cosx + 2(1 - cos^2x)

Distribute the 2 on the right side.

1 - 2cos^2x = sinx * cosx + 2 - 2cos^2x

Combine like terms.

1 = sinx * cosx + 2

Subtract 2 from both sides.

-1 = sinx * cosx

Now, we have the equation -1 = sinx * cosx.

This equation does not have a simple solution. It is a transcendental equation that cannot be solved algebraically. However, we can use numerical methods or graphical methods to approximate the solutions.