Cosx*tgx-ctgx-sinx=0

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To solve the equation cos(x)tan(x) - cot(x) - sin(x) = 0, we can rewrite it using trigonometric identities.

Recall that cot(x) = 1/tan(x) and sin(x) = 1/csc(x). Therefore, the equation becomes:

cos(x)tan(x) - 1/tan(x) - 1/csc(x) = 0

Next, convert tan(x) and csc(x) into sine and cosine functions:

cos(x)sin(x)/cos(x) - 1/(sin(x)/cos(x)) - 1/(1/sin(x)) = 0
sin(x) - cos(x) - sin(x) = 0

Simplify the equation:

-sin(x) - cos(x) = 0

Now, you can substitute cos(x) = √(1 - sin^2(x)) into the equation:

-sin(x) - √(1 - sin^2(x)) = 0

Square both sides to eliminate the square root:

sin^2(x) + sin(x) + 1 = 0

This is a quadratic equation in terms of sin(x). You can solve it using the quadratic formula or factoring method to find the values of sin(x) that satisfy the equation.