2. Let 1 1 (–18 sin t – 16 cos t 0 3 0 1 A = f(t) = -25 cos t 1 -25 sin t Find the general solution to ' = Aã + f.

Q: Solve the cos - 4 = sin 0 - 5 equation for 0 < 0 < 2π.

A:

Q: (cos(80) + i sin(80)) 2.

A:

Q: Prove that sin(x + y) sin(x − y) = sin²x − sin²y. -

A: Formula's

Q: Solve 6 cos(2t) = 6 sin?(t) + 3 for all solutions 0 <t < 27. t = Give your answers accurate to at…

A: Formula used: cos(2t)=1-2sin(t) Signs of trigonometric ratios: In the first quadrant: All are…

Q: cos t 1-sin t sect + tant

A:

Q: If A = A-1 = 2e2t sin(5t) 2e²t cos(5t) 2e5t cos(5t) -2est sin(5t) , then 4

A:

Q: 3. Solve cos 2x +3 sin x– 2 = 0, 0° < x< 360°.

A:

Q: 1. A. f sin 2x cos 5x dx B. f cos 2x cos 3x dx c. ftan³x sec5x dx

A:

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 7. Determine all the solutions to the equation in the interval [0, 27): sin 20 cos0 – cos 20 sin0 +1…

A: As we know that Sinx-y=SinxCosy-CosxSinyThe genaral solution of Sinz=-1  then z=Sin-1-1=nπ±π2

Q: Cannot solve

A: To find the value

Q: Find cos(u+v) sinu= -4/5 with 3pi/2 &lt;u&lt;2pi and cosv= -5/13 with pi/2 &lt;v&lt;pi

A: u is in the fourth quadrant. There cos will be positive.

Q: (b) cos³ (2t) sin¯4 (2t) dt

A:

Q: 2 sin2x – 3 = 3 cos x and 90° < x < 270°

A: Hello , thanks for your question as it is not clear mentioned that it is Sin2 x or sin 2x So we are…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.