$(sec x - tan x)^2 \\ \\ = sec^2x - 2 sec x tan x + tan^2 x \\ \\ =(1+tan^2 x) - 2 sec x tan x +tan^2 x \\ \\ =1 - 2 sec x tan x + 2 tan^2 x \\ \\ = 1 - 2tan x(sec x - tan x) \\ \\ =1 - \frac{2 sin x}{cos x} (\frac{1-sin x}{cos x}) \\ \\ = 1 - \frac{2 sin x (1-sin x)}{cos^2 x} \\ \\ =1 - \frac{2 sin x (1-sin x)}{1-sin^2 x} \\ \\ =1 - \frac{2 sin x (1-sin x)}{(1-sin x)(1+sin x)} \\ \\ =1-\frac{2 sin x}{1+sin x}$

3 0

3 years ago

The state of New Jersey makes approximately $1.55 billion annually from tolls of the $1.55 billion about 3/4 comes from tolls on

Rama09 [41]

Percent of turn pike is 75% and percent of parkway is 25%.

Solution:

Given, The state of New Jersey makes approximately $1.55 billion annually from tolls of the $1.55 billion

About $\frac{3}{4}$ comes from tolls on the turnpike

Remaining $\frac{1}{4}$ comes from tolls on the parkway

To find the percent of the total revenue from turnpike:

$\begin{array}{l}{\text { Percent of turnpike }=\frac{\text { amount from parkway }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{3}{4} \text { of total revenue }}{\text { tot al revenue }} \times 100} \\\\ {=\frac{\frac{3}{4} \times \text { total revenue }}{\text { total revenue }} \times 100} \\\\ {=\frac{3}{4} \times 100=3 \times 25=75 \%}\end{array}$

To find the percent of the total revenue from parkway:

$\begin{array}{l}{\text { Percent of parkway }=\frac{\text { amount from parkway }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{1}{4} \text { of total revenue }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{1}{4} \times \text { total revenue}}{\text { total revenue }} \times 100} \\\\ {=\frac{1}{4} \times 100=25 \%}\end{array}$

Summarizing the results:

Percent of turn pike is 75%

Percent of parkway is 25%

3 0

3 years ago