If sin/cos = tan, would tan(sin) = cos? if not explain?

Short no.

You need to be a little careful with notation here. Sin, cos, and tan are function names. As such, we usually expect tan(sin) to mean "sin" is the argument of the tan function. It will only be equal to cos for some specific angles.

More carefully written, you have

... tan(θ) = sin(θ)/cos(θ)

Then, it is true that

... tan(θ)(cos(θ)) = sin(θ) . . . . . for cos(θ) ≠ 0

For this, the parentheses around cos(θ) mean it is a factor in the product whose other factor is tan(θ).

In general,

... tan(θ)(sin(θ)) ≠ cos(θ)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

explanation:

step-by-step explanation: