1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SVETLANKA909090 [29]
2 years ago
5

Prove that : 1/1-secA + 1/1+secA = -2cot^2A​

Mathematics
1 answer:
irina1246 [14]2 years ago
7 0

Answer:

Step-by-step explanation:

LHS = 1/1-secA + 1/1+secA

       = \frac{1*(1+Sec A)}{(1-Sec A)(1+Sec A)}+\frac{1*(1-Sec A)}{(1+Sec A)*(1-Sec A)}\\\\=\frac{(1+Sec A)}{1-Sec^{2} A}+\frac{(1-Sec A)}{1-Sec^{2} A}\\\\=\frac{1+Sec A+1-Sec A}{(1-Sec^{2} A)}\\\\= \frac{2}{(1-Sec^{2} A)}\\\\=\frac{2}{-(Sec^{2} A - 1)}\\\\= \frac{-2}{Tan^{2} A}\\\\= -2Cot^{2} A

You might be interested in
27 solid iron spheres,each of radius x cm are melted to form a sphere with radius y cm ,find the ratio of x:y
madam [21]

Radius of 1 solid iron sphere =r

→ Volume =34πr3

→ Volume of 27 solid iron

spheres =27x34πr3

→ 34πr'3=27x34πr3

r'3=2πr3

→r'=3r

(ii) Surface area =4+πr2

SA r'=4πr'2

=4π(3r)2=36πr2

S'S=36πr24πr2=91=1:9

7 0
2 years ago
A teacher keeps track of how many books are read by students in each class .which grade has read a higher rate of books per stud
Vadim26 [7]
7 grade needs to read 94 more books in order to catch up with 6 grade.

3 0
3 years ago
Help!!!!!!!!!!!!!!!!!!!!
Sauron [17]
21 not sure but you can do it
6 0
3 years ago
How do you do this question?
Molodets [167]

Answer:

C. y₂ = (1 + (t/n))²

Step-by-step explanation:

yₙ₊₁ = yₙ + Δt F(tₙ, yₙ)

yₙ₊₁ = yₙ + Δt yₙ

yₙ₊₁ = yₙ + (t/n) yₙ

When n=0:

y₁ = y₀ + (t/n) y₀

y₁ = 1 + (t/n)

When n=1:

y₂ = y₁ + (t/n) y₁

y₂ = 1 + (t/n) + (t/n) (1 + (t/n))

y₂ = 1 + (t/n) + (t/n) + (t/n)²

y₂ = 1 + 2(t/n) + (t/n)²

y₂ = (1 + (t/n))²

4 0
3 years ago
What is the range of the following function:<br> y = 2(5^x) - 1
Orlov [11]
<h2>Hello!</h2>

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

<h2>Why?</h2>

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

5 0
3 years ago
Other questions:
  • Given that y=18 + 3x² (i) find the value of y when x= -2
    8·2 answers
  • An apple weighs 350 grams. a pear weighs 0.4 kilograms. Which of the following statements are true. (2 answers)
    10·2 answers
  • Dave has $13 to spend on a $4 book and two birthday cards (c) for his friends. How much can he spend on each card if he buys the
    9·2 answers
  • Dylan is planting flower boxes to decorate the school entrance. He has 64 marigolds and 72 periwinkles. Each flower box must con
    8·1 answer
  • Which expression converts StartFraction pi Over 4 EndFraction radians to degrees?
    8·2 answers
  • 1.-4x+7=11 2. 17=5y-3
    14·2 answers
  • A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invo
    15·1 answer
  • Write 6.38612 correct to 2 decimal places.​
    14·1 answer
  • jason and ben are coworkers five years ago jason was 2.5 times as old as ben if ben is 31 how old is jason]
    12·1 answer
  • The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!