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
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.

You might be interested in
HELP PLEASE Sam and George both worked hard over the summer. Together they earned a total of $525. George earned $75 more than S
ZanzabumX [31]

Answer:   Sam = $225      George = $300

<u>Step-by-step explanation:</u>

NOTES:

Sam: s

George: g = s + 75

Together: s + g = 525


a.

The two equations that can be created are "George" and Together"

The system is: \left \{ {{\text{g = s + 75}} \atop {\text{s + g = 525}}} \right.

b.

see attached graph

c.

The intersection of the two lines is at (225, 300).  Since Sam represented the x-axis and Georege represented the y-axis, then Sam = $225 and George = $300.


BONUS:

This system can also be solved algebraically using the substitution method.

Replace "g" with "s + 75" into the second equation:

s + (s + 75) = 525

2s + 75 = 525

2s = 450

 s = 225

Next, input the s-value into the George equation to solve for g:

g = s + 75   = (225) + 75   = 300

5 0
2 years ago
A cable installer charges $30.00 per hour plus a $50.00 service charge. Your father's firm hires him to hookup his company's int
vladimir1956 [14]
30*8.5=255 255+50=$305
4 0
3 years ago
Read 2 more answers
How do I put y=90-15x in standard form
lisabon 2012 [21]

The standard form: Ax + By = C


y = 90 - 15x     <em>add 15x to both sides</em>

<h3>15x + y = 90</h3>
8 0
3 years ago
I need help I did most of them but not sure if there right if you could tell me that would be great. Also can you help me with 9
Andrej [43]

Explanation:

In the given identified the following with reasons.

1. Given

2. Corresponding Angles postulate

3. Reflexive property of congruence

4. AA similarity postulate.

5. Triangle proportionate  

6. Cross multiply

7. Distributive property of equality

8. Subtraction property of equality

9. Division property of equality

10. Prove

8 0
3 years ago
Joseph built a model of a pyramid where
monitta

Answer:

7

Step-by-step explanation:

\sqrt{49}  = 7

4 0
2 years ago
Other questions:
  • Plzzzz help
    9·2 answers
  • A line passes through the point (0, –1) and has a slope of -2/3 What is the equation of the line?
    12·1 answer
  • the ratio of the number of adults to the number of students at the prom has to be 1:10. Last year there were 477 more students t
    9·1 answer
  • sallys baked beans recipe calls for 5 pounds of sugar and 20 pounds of dried beans. How many pounds of sugar are needed for a re
    14·1 answer
  • Incoming students at a school are assigned six-digit ID numbers. The first digit is chosen at random from the digits 0 through 3
    9·2 answers
  • Round 15.6895 to the nearest tenth<br><br> A) 15.7<br> B) 15.6<br> C) 15.68<br> D) 15.69
    5·2 answers
  • Can someone please help me with this?
    8·2 answers
  • A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a​ single-strand electric
    6·1 answer
  • Find K if x + 1 is a factor of P(x) = Kx^2-x+2
    14·1 answer
  • Alec says the sum of two numbers can never be less than either number.Use a model to explain why Alex is incorrect.​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!