Someone help me with proving identities? and please show the work if you can!

See Below.

Step-by-step explanation:

11)

We have:

Rewrite:

Multiply:

Combine:

According to the Pythagorean Identity, sin²θ + cos²θ = 1. Hence:

Simplify:

12)

We have:

Pythagorean Identity:

From the Pythagorean Identity, if we divide both sides by cos²θ, we acquire that tan²θ + 1 = sec²θ. Hence:

Simplify:

13)

We have:

Rewrite:

Multiply both top and bottom by cosθsinθ. Hence:

By the Pythagorean Identity:

Simplify:

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet