We are to verify the identity:
cos(α-B)-cos(α+B) = 2 sinα sinβ
Left hand side = cos(α - B)-cos(α + B)
= cosα cosβ + sinα sinB - (cosα cosB - sinα sinβ)
= cosα cosβ + sinα sinB - cosα cosB + sinα sinβ)
= sinα sinβ + sinα sinβ
= 2 sinα sinβ
= Right Hand side
Answer:
Given : BRDG is a kite that is inscribed in a circle,
With BR = RD and BG = DG
To prove : RG is a diameter
Proof:
Since, RG is the major diagonal of the kite BRDG,
By the property of kite,
∠ RBG = ∠ RDG
Also, BRDG is a cyclic quadrilateral,
Therefore, By the property of cyclic quadrilateral,
∠ RBG + ∠ RDG = 180°
⇒ ∠ RBG + ∠ RBG = 180°
⇒ 2∠ RBG = 180°
⇒ ∠ RBG = 90°
⇒ ∠ RDG = 90°
Since, Angle subtended by a diameter or semicircle on any point of circle is right angle.
⇒ RG is the diameter of the circle.
Hence, proved.
<span>This polygon is composed of a right triangle and <span>a parallelogram.
The area of right angle :

The area of the </span></span><span>parallelogram</span>:

The area of the polygon is equal:

Therefore, the answer is:
Yes it will. For every one hour, the train travels 170 miles. That’s the rate of change/ the ratio-> 1:170
1 hour=3600 seconds
8 times 3600 =28800