Mathematics: 20 points & Brainliest to the one who gets ALL of them correct! NEED HELP ASAP Verify these Identities & SHOW YOUR WORK: 1. cosx−cosxsin²x = cos³x 2. = 3. cos⁴b−sin⁴b = 1−2sin²b 4. = 5. (secx−tanx)² = HELP!!!

20 points & Brainliest to the one who gets ALL

davestrider404

29.07.2021

The area of rhombus PQRS is 120 m.

Step-by-step explanation:

Consider the rhombus PQRS.

All the sides of a rhombus are equal.

Hence, PQ = QR = RS = SP = 13 m

The diagonals PR and QS bisect each other.

Let the point at of intersection of the two diagonals be denoted by X.

Consider the triangle QXR.

QR = 13 m

XR = 12 m

The triangle QXR is a right angled triangle.

Using the Pythagorean theorem compute the length of QX as follows:

QR² = XR² + QX²

QX² = QR² - XR²

= 13² - 12²

= 25

QX = √25

= 5 m

The measure of the two diagonals are:

PR = 2 × XR = 2 × 12 = 24 m

QS = 2 × QX = 2 × 5 = 10 m

The area of a rhombus is:

$\text{Area}=\frac{1}{2}\times d_{1}\times d_{2}$

Compute the area of rhombus PQRS as follows:

$\text{Area}=\frac{1}{2}\times PR\times QS$

$=\frac{1}{2}\times 24\times 10\\\\=120$

Thus, the area of rhombus PQRS is 120 m.

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