Question

Cosx*tgx-ctgx-sinx=0

Answer 1

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Answer 2

To solve the equation cos(x) * tan(x) - cot(x) - sin(x) = 0, we'll simplify it step by step:

1. Recall the trigonometric identities:

   • tan(x) = sin(x) / cos(x)
   • cot(x) = 1 / tan(x) = cos(x) / sin(x)

2. Substitute these identities into the equation: cos(x) * (sin(x) / cos(x)) - (cos(x) / sin(x)) - sin(x) = 0

3. Simplify the equation: sin(x) - cos(x) - sin(x) = 0

4. Combine like terms: -cos(x) = 0

5. Solve for x: cos(x) = 0

The solutions to the equation cos(x) = 0 occur when x is equal to π/2 + nπ or 3π/2 + nπ, where n is an integer.

So the solutions to the equation cos(x) * tan(x) - cot(x) - sin(x) = 0 are: x = π/2 + nπ or 3π/2 + nπ, where n is an integer.