$\displaystyle \frac{2\sin{A}}{\cos{3A}}\\\\=\frac{2\sin{A}\cos{A}}{\cos{3A}\cos{A}}\qquad\text{multiply by cos(A)/cos(A)}\\\\=\frac{\sin{2A}}{\cos{3A}\cos{A}}\qquad\text{double angle formula for sin}\\\\=\frac{\sin{(2A-A)}}{\cos{3A}\cos{A}}=\frac{\sin{3A}\cos{A}-\cos{3A}\sin{A}}{\cos{3A}\cos{A}}\\\\=\tan{3A}-\tan{A}$

Then the sum of the three terms on the left is

$\left(\tan{3A}-\tan{A}\right)+\left(\tan{9A}-\tan{3A}\right)+\left(\tan{27A}-\tan{9A}\right)\\\\=\tan{27A}-\tan{A}\qquad\text{Q.E.D.}$

4 0

3 years ago

5x - y = -38 3x + 4y =0 (4,3) (-4,3) (4,-3) (-4,-3)

Mice21 [21]

Answer:

(-4,-3)

Step-by-step explanation:

7 0

2 years ago

Which property of equality is represented? If x = 5, then 5 = x.

Brut [27]

x=5 5=x should be reflexive property

6 0

3 years ago

A contestant on a game show must choose 2 of 16 boxes. Once a box is chosen, it is removed from the game. Of the 16 boxes, 3 con

Inessa05 [86]

Answer:

7 / 30

Step-by-step explanation:

This is a selection without replacement probability :

Total boxes = 16

With money = 3

With traveling prices = 5

Empty = 8

P(choosing 2 empty boxes) :

P(empty) * P(empty)

P(empty) = Number of empty boxes / total number of boxes

First pick = empty

P(empty) = 8 / 16 = 1/2

Without replacement :

Second pick = empty

P(empty) = 7 / 15

P(choosing 2 empty boxes) = 1/2 * 7/15 = 7 /30

7 0

2 years ago