1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form d=sinw(t) for the simple harmonic motion.

2) Verify the identity
tan^2X-cot^2X/tanX+cotX=tanX-cotX

I'm not completely sure on the first one, but I think it looks like
d=sin(264*t) Check your text for a worked example.
The second one is algebra.
[(tanX)^2-(cotX)^2]/[tanX+cotX]=tanX-cotX
or
[(tanX-cotX)(tanX+cotX)]/[tanX+cotX]=tanX-cotX
Can you finish it?

Absolutely! Here's the continuation of the second problem:

[(tanX-cotX)(tanX+cotX)]/[tanX+cotX]=tanX-cotX

Since (tanX+cotX) appears in both the numerator and denominator, we can cancel it out:

(tanX-cotX) = tanX-cotX

And just like that, the identity is verified! It seems like X wanted to be left alone.

1) The correct equation for simple harmonic motion can be written as d = A * sin(ω * t), where A represents the amplitude of the motion and ω represents the angular frequency. Since the problem states that middle C has a frequency of 264 vibrations per second, we can calculate the angular frequency as follows:

ω = 2π * f
ω = 2π * 264
ω ≈ 1661.226

Therefore, the equation for simple harmonic motion is d = A * sin(1661.226 * t).

2) Continuing from where you left off:

[(tanX - cotX)(tanX + cotX)] / (tanX + cotX) = tanX - cotX

Now cancel out (tanX + cotX) on both sides:

tanX - cotX = tanX - cotX

As both sides of the equation are the same, the identity is verified.

Certainly! Let's continue solving the second problem.

[(tanX-cotX)(tanX+cotX)]/[tanX+cotX]=tanX-cotX

We can simplify the left side of the equation by canceling out the (tanX+cotX) terms:

(tanX-cotX) = tanX-cotX

We can see that both sides of the equation are equal, which means the identity is verified.

Therefore, the given identity is correct.