(tanθ + cotθ)² = sec²θ + csc²θ
<u>Expand left side</u>: tan²θ + 2tanθcotθ + cot²θ
<u>Evaluate middle term</u>: 2tanθcotθ = 
= 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
<u>Apply trig identity:</u> tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
<u>Apply trig identity:</u> 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
Answer:
Step-by-step explanation:
let x be the population
so we have ,
2x= 6h
?= 3 days or 3×24h
by cross multiplication we have
2x× 72h= 6h×?
?= 2x×72/6 = 24x
So, in three days the bacteria will b 24 times current population.
Answer:
A. Option 1
Sign up cost = 0
1 Month = 125
2 Months = 150
3 Months = 175
4 Months = 200
Step-by-step explanation:
For every option simply write what the starting cost is in the top box for every option. Then multiply the monthly cost by how many months for each box and then add the starting cost. The result of the multiplication and addition will be what you put in each box.
Answer:
Step-by-step explanation:
Total amount of apples that Nicole bought was 6 pounds.
Each pound of apple cost $1.50
This means that the total cost of the 6 pounds of apple that Nicole bought would be
6 × 1.5 = $9
The store had a discount of $2 off her total purchase. This means that the amount that was paid is
9 - 2 = $7
If Nicole and her friend then divided the cost of the purchase evenly, let x represent the amount that each of them would pay. Therefore, the expression that can be used to determine how much Nicole and her friend each paid for the apples would be
x = 7/2
Answer: - 49
Step-by-step explanation:
f(x) = -2x - 1
g(x) = 
- 1
fg(x) = f ( - 1) , we just put in the value of g(x) , the next thing is to substitute - 1 for the value of x in f(x) , that is
fg(x) = -2( - 1) - 1
fg(x) = -2 + 2 - 1
fg(x) = -2 + 1
Therefore : fg(-5) means we will substitute -5 for x in fg(x) , that is
fg(-5) = -2 (
+ 1
fg(-5) = -2(25) + 1
fg(-5) = -50 + 1
fg(-5) = -49
