Question

(2sint-3cost)/(2cost-3sint)=3     ctg-?

Answer 1

  $\frac{2sint-3cost}{2cost-3sint}=3$ 
Разделим числитель и знаменатель на sint ,  $sint\ne 0$.

$\frac{2-3ctgt}{2ctgt-3}=3\; \; \to \; \; 2-3ctgt=3(2ctgt-3)\\\\2-3ctgt=6ctgt-9\\\\9ctgt=11\\\\ctgt=\frac{11}9}$

Answer 2

To solve the equation (2sin(t) - 3cos(t))/(2cos(t) - 3sin(t)) = 3 and find the value of cotangent (ctg), we can simplify the expression and manipulate it to isolate ctg. Here's how:

1. Start with the given equation: (2sin(t) - 3cos(t))/(2cos(t) - 3sin(t)) = 3

2. Multiply both sides of the equation by (2cos(t) - 3sin(t)) to eliminate the denominator: (2sin(t) - 3cos(t)) = 3(2cos(t) - 3sin(t))

3. Expand the right side: 2sin(t) - 3cos(t) = 6cos(t) - 9sin(t)

4. Rearrange the equation to group similar terms: 2sin(t) + 9sin(t) = 6cos(t) + 3cos(t)

5. Combine the terms: 11sin(t) = 9cos(t)

6. Divide both sides by cos(t): 11sin(t)/cos(t) = 9

7. Use the trigonometric identity tan(t) = sin(t)/cos(t): 11tan(t) = 9

8. Divide both sides by 11: tan(t) = 9/11

9. Finally, find the cotangent (ctg) by taking the reciprocal of the tangent: ctg(t) = 1/tan(t) ctg(t) = 1/(9/11) ctg(t) = 11/9

Therefore, ctg(t) is equal to 11/9.