Prove that,
(1+sin theta + cos theta) ^2 = 2(1+sin theta) (1+cos theta)

Proof below

Step-by-step explanation:

Trigonometric Identities

Before we prove the given identity, we need to recall:

We have to prove that:

Let's expand the square on the left side as indicated in the formula above:

Recall the fundamental trigonometric identity:

Substituting and operating:

Factoring by 2:

Factoring cos θ in the last two terms:

Factoring

Proven

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6