Question

1-(sin(d)+cos(d))^2/sin(d)cos(d)-ctg(d)

Answer 1

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Answer 2

To simplify the expression, let's work step by step:

1. Start by expanding the square of the binomial (sin(d) + cos(d))^2: (sin(d) + cos(d))^2 = sin^2(d) + 2sin(d)cos(d) + cos^2(d)

2. Now rewrite the original expression using the expansion: (1 - (sin(d) + cos(d))^2) / (sin(d)cos(d) - ctg(d)) = (1 - (sin^2(d) + 2sin(d)cos(d) + cos^2(d))) / (sin(d)cos(d) - ctg(d))

3. Simplify the numerator (1 - (sin^2(d) + 2sin(d)cos(d) + cos^2(d))) using trigonometric identities: 1 - (sin^2(d) + 2sin(d)cos(d) + cos^2(d)) = 1 - (1 + cos(2d)) = -cos(2d)

4. Now the expression becomes: -cos(2d) / (sin(d)cos(d) - ctg(d))

5. Rewrite cotangent (ctg) in terms of sine and cosine: ctg(d) = 1 / tan(d) = cos(d) / sin(d)

6. Substitute ctg(d) with cos(d)/sin(d) in the expression: -cos(2d) / (sin(d)cos(d) - cos(d)/sin(d))

7. Find a common denominator for the denominator: -cos(2d) / (sin^2(d)cos(d) - cos^2(d)/sin(d))

8. Now simplify further by using trigonometric identities: sin^2(d) + cos^2(d) = 1, and cos(2d) = 2cos^2(d) - 1 -cos(2d) = -2cos^2(d) + 1

9. Substitute the identities in the expression: (-2cos^2(d) + 1) / (sin^2(d)cos(d) - cos^2(d)/sin(d))

10. Factor out common terms from the denominator: (-2cos^2(d) + 1) / [(cos^2(d)sin(d) - cos^2(d))/sin(d)]

11. Cancel out common terms in the denominator: (-2cos^2(d) + 1) / (cos^2(d) - cos^2(d)) = (-2cos^2(d) + 1) / 0

Now, we have an expression with 0 in the denominator. Division by zero is undefined, so the simplified expression is undefined for the given input.