From the trigonometry:

tan θ = (sin θ) / (cos θ)
cot θ = (cos θ) / (sin θ)

∴ tan θ + cot θ = (sin θ) / (cos θ) + (cos θ) / (sin θ)
= [ sin² θ + cos² θ]/( sin θ cos θ) = 1 /( sin θ cos θ )

note : sin² θ + cos² θ = 1

6 0

3 years ago

A store finds that the number of shirts sold increases each week. In the first week, only 15 shirts were sold. In the next week,

nikklg [1K]

Answer:

$a_n=8+7n$

Step-by-step explanation:

No. of T-Shirts sold in first week = 15

No. of T-Shirts sold in second week = 22

No. of T-Shirts sold in third week = 29

The number of shirts sold each week represents an arithmetic sequence.

15,22,29,....

So, a = first term = 15

d = common difference = 22-15= 29-22= 7

Formula of nth term : $a_n=a+(n-1)d$

a is the first term

d is the common difference

n is the number of term

Now substitute the values in the formula :

$a_n=15+(n-1)7$

$a_n=15+7n-7$

$a_n=8+7n$

Where n is the number of weeks

Hence the explicit rule for the arithmetic sequence that defines the number of shirts sold in week n is $a_n=8+7n$

8 0

3 years ago

Find the slope of line with the given points (6, - 4)(1, 5)

ddd [48]

Answer:

-9/5 is the slope

Step-by-step explanation:

5-(-4)=9

1-6=-5

7 0

3 years ago