Prove sin theta= tan theta/ sqrt 1+tan^2 theta. hint: solve for sin^2 in number 14.

here is number 14:
sin^2 theta/ 1-sin^2 theta= tan^2 theta

If you know all the trig identities you don't need to solve 14. The trig identities you need to know are tan=sin/cos. Sec=1/cos. And 1+tan^2= sec^2
(I'll be replacing theta with x to make it easier to type)

Problem: sinx=tanx/sqrt 1+tanx^2.

Since 1+tanx^2=secx ^2

Sinx=tanx/sqrt secx^2

Sinx=tanx/secx

Now tanx= sinx/cosx and secx=1/cosx
(Sinx/cosx)/(1/cosx). The cosx cancel out leaving sin

So sinx=sinx

V = 1200π

Step-by-step explanation:

Volume of a cylinder formula:

V = πr²h

Let's find the height of the cylinder by multiplying 20 cm by 3/5.

20 * 3/5 = 60/5 = 12 cm

The radius is 1/2 of the diameter, so:

20 * 1/2 = 20/2 = 10 cm

Substitute 12 for h and 10 for r into the volume formula.

V = π(10)²(12)

Simplify.

V = π * 100(12)  V = π * 1200

The volume of a cylinder, in terms of π, is V = 1200π.