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Ivenika [448]
3 years ago
15

Verify the identity

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0

<u>Given</u>:

Given that we need to prove the identity \sin x+\sin x \tan ^{2} x=\tan x \sec x

<u>Proof</u>:

Step 1: Factor out the common term sin x, we get;

\sin x\left(1+\tan ^{2} x\right)=tan \ x \ sec \ x

Step 2: Using the identity 1+tan^2 x=sec^2x

\sin x \sec ^{2} x=tan \ x \ sec \ x

Step 3: Reciprocating sec x, we get;

\sin x \cdot \frac{1}{\cos ^{2} x}=tan \ x \ sec \ x

Step 4: Splitting the denominator, we have;

\frac{\sin x}{\cos x} \cdot \frac{1}{\cos x}=tan \ x \ sec \ x

Simplifying, we get;

\tan x \sec x=\tan x \sec x

Thus, the identity is proved.

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Find the error and then find the correct answer.​
qaws [65]

Answer:

  • w = 3

Step-by-step explanation:

<u>The correct one is given below:</u>

- 5 - 4w = - 17

<u>+5            + 5</u>

     -<u> 4</u>w = <u>-12</u>

      - 4      -4          

        w = 3

The error is 4w instead of - 4w

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2 years ago
How many quarts are there in 10 1/2 Gallons
umka2103 [35]
42 quarts is the answer
4 0
3 years ago
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What is the perimeter of the triangle (4,1) (2,5) (1,-1)
Naya [18.7K]

the perimeter of the triangle=14.38

The coordinates of the triangle (4,1),(2,5),(1,-1);

In geometry, the perimeter of a shape is defined as the total length of its boundary.

The perimeter of the triangle is the sum of all the sides of the triangle =a+b+c (assuming a,b, and c are the sides of the triangle)

By using the distances formula find the length of the sides of the triangle:√[(x₂ - x₁)² + (y₂ - y₁)²],

where (x₁,y₁),(x₂,y₂) are the coordinates ,

a=√[(4 - 2)² + (1- 5)²] = \sqrt 20=4.7

b=√[(2 -1)² + (5 -(-1))²]=\sqrt37=6.08

c=√[(1 -4)² + ((-1)-1)²]=\sqrt13=3.60

the perimeter of the triangle=a+b+c=4.7+6.08+3.60=14.38

hence ,perimeter of the triangle=14.38

Learn more about perimeter of triangle:

brainly.com/question/23935199

3 0
1 year ago
Is -6.175 is an irrational number?
kipiarov [429]
No.

Any number you can write completely is a rational number.
Any number with a repeating decimal fraction is also a rational number.
___
Any number that goes on forever without repeating is an irrational number. These are usually represented symbolically (because they cannot be written "exactly" any other way). These include such numbers as √2, π, e, ∛(-4), and an infinite number of others.
4 0
3 years ago
Convert the following numbers of calories or
kap26 [50]

Answer:

  • 32.823 kJ
  • 190.4 kJ
  • 260.00 kJ
  • 180.012 kJ

Step-by-step explanation:

The conversion factor for food energy or thermochemical calorimetry* is ...

  1 calorie = 4.184 J

  1000 calorie = 4.184 kJ

__

a. 7845 cal = 7845·4.184 J = 32,823 J = 32.823 kJ

b. 4.55·10^4 cal = 4.55·10^4·4.184 J = 1.904·10^5 J = 190.4 kJ

c. 62.142 kcal = 62.142·4.184 kJ = 260.00 kJ

d. 43,024 cal = 43,024·4.184 J = 180,012 J = 180.012 kJ

_____

* The thermochemical calorie is defined in terms of the heat capacity of water. An international calorie of 4.1868 J is defined in terms of energy, without respect to the heat capacity of water.

6 0
3 years ago
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