Question

2sint-3cost/2cost-3sint=3

Answer 1

2sint-3cost=3*( 2cost-3sint)
11sint-9cost=0поделим наcost≠0
11tgt-9=0
tgt=9/11
t=arctgt+πn

Answer 2

To solve the equation 2sin(t) - 3cos(t) / (2cos(t) - 3sin(t)) = 3, we can start by multiplying both sides of the equation by the denominator (2cos(t) - 3sin(t)) to eliminate the fraction:

(2sin(t) - 3cos(t)) * (2cos(t) - 3sin(t)) / (2cos(t) - 3sin(t)) = 3 * (2cos(t) - 3sin(t))

Simplifying the left side of the equation:

(2sin(t) - 3cos(t)) * (2cos(t) - 3sin(t)) = 6cos(t) - 9sin(t)

Expanding the product on the left side:

4sin(t)cos(t) - 6sin^2(t) - 6cos^2(t) + 9sin(t)cos(t) = 6cos(t) - 9sin(t)

Combining like terms:

13sin(t)cos(t) - 6(sin^2(t) + cos^2(t)) = 6cos(t) - 9sin(t)

Using the trigonometric identity sin^2(t) + cos^2(t) = 1:

13sin(t)cos(t) - 6(1) = 6cos(t) - 9sin(t)

Simplifying further:

13sin(t)cos(t) - 6 = 6cos(t) - 9sin(t)

Bringing all the terms to one side of the equation:

13sin(t)cos(t) + 9sin(t) - 6cos(t) - 6 = 0

Now, we can factor out common terms:

(13cos(t) - 6)(sin(t) + 1) - 6 = 0

Expanding:

13cos(t)sin(t) + 13cos(t) - 6sin(t) - 6 - 6 = 0

13cos(t)sin(t) - 6sin(t) + 13cos(t) - 12 = 0

Now, we can rearrange the terms:

(13cos(t) - 6sin(t)) + (13 - 12) = 0

13cos(t) - 6sin(t) + 1 = 0

Therefore, the equation 2sin(t) - 3cos(t) / (2cos(t) - 3sin(t)) = 3 simplifies to 13cos(t) - 6sin(t) + 1 = 0.