(a) Write cos 3x + i sin 3x = e^(3ix) = (cos x + i sin x)^3 by Euler's formula, expand, and equate real and imag inary parts to derive the identities, cos^(3) x = 3/4 cos x + 1/4 cos 3x, sin^(3) x = 3/4 sin x - 1/4 sin 3x (b) Use the result of part (a) to find a general solution of y'' + 4y = cos^(3) x.

Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1), help please

A consumer in a grocery store pushes a cart with a force of 35 N directed at an angle of ${\displaystyle {25}^{\circ }}$ below the horizontal. The force is just enough to overcome various frictional forces, so the cart moves at a steady pace. Find the work done by the shopper as she moves down a ${\displaystyle 50.0-m}$ length aisle.

What is the derivative of ${\displaystyle \arcsin \left[x^{\frac{1}{2}}\right]}$?

What is the derivative of ${\displaystyle y=\arcsin \left(\frac{3x}{4}\right)}$?

Determine if the graph is symmetric about the $x$-axis, the $y$-axis, or the origin.$r=4\cos 3\theta$.

How to differentiate ${\displaystyle 1+{\cos }^2\left(x\right)}$?

What is the domain and range of ${\displaystyle \left|\cos x\right|}$?

How to find the value of ${\displaystyle \csc 74}$?

How to evaluate ${\displaystyle \sec \left(\pi \right)}$?

Using suitable identity solve (0.99)raised to the power 2.

How to find the derivative of ${\displaystyle y=\tan \left(3x\right)}$?

Find the point (x,y) on the unit circle that corresponds to the real number t=pi/4

How to differentiate ${\displaystyle {\sin }^{3}x}$?

A,B,C are three angles of triangle. If A -B=15, B-C=30. Find A , B, C.

Find the value of $\sin {270}^{\circ }$.