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
Maru [420]
2 years ago
15

Show that sec(x)-tan(x)sin(x)=cos(x)is an identity for any value of x.

Mathematics
1 answer:
Dmitriy789 [7]2 years ago
3 0

Here is one way to show that the left side is identical to the right side.

\sec(x)-\tan(x)\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)}\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{1-\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{\cos^2(x)}{\cos(x)} = \cos(x)\\\\\\\cos(x)=\cos(x)\\\\\\

Throughout the entire process, the right hand side stayed the same. When working on identities, it's important to keep one side the same while you transform the other side.

Despite the two sides being identical when simplified, there is the issue of cos(x) being zero in the denominator on the left hand side. Be sure to account for this when forming the domain. No such issue occurs on the right hand side. For instance, the value x = pi/2 leads to a division by zero error when in radian mode. So if I was your teacher, I would revise the "for any value of x" and replace it with something along the lines of "for any x value in the domain".

You might be interested in
The picture shows a triangular island: Which expression shows the value of c?
anyanavicka [17]

Answer:

c = b / cos 45.

Step-by-step explanation:

cos 45 = b/c

c * cos 45 = b

c = b / cos 45.

5 0
3 years ago
1.Mr. Redding sells vehicles to 40% of the people that come to the sales lot. If 165 people came to the lot last month, how many
Vanyuwa [196]
He would have sold 66 vehicles
6 0
2 years ago
Help please 6+6x4+8.................
Natasha_Volkova [10]
,12x12=144.................
6 0
3 years ago
Read 2 more answers
Use a trigonometric function to find the value of x
Alex17521 [72]

(180-30)/2 would be the equation and the answer is 150/2

5 0
3 years ago
HELP WILL GIVE BRAINLIEST
AnnyKZ [126]
<h2>Good evening ,</h2>

<em><u>Answer</u></em>:

q=-10

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

D:y=-3x+q

let’s find q

A(-4,2)∈D ⇔ 2=-3(-4)+q ⇔ q=-10

then D:y=-3x-10

look at the photo for more details.

______________

:)

5 0
2 years ago
Other questions:
  • 13) -4= -b -1/3b and -23/3= 1/2a + 5/3a
    9·1 answer
  • A coach needs to rank his top 2 players in order. How many possible ways can this be done if there are 25 boys on the team?
    11·1 answer
  • WILL MARK BRAINLIEST PLEASE HELP! How many three-digit numbers are multiples of neither 5 nor 7?
    7·2 answers
  • Bobcat Park is a rectangular park with an area of 5 2/5 square miles.Its width is 1 11/25 miles.How long is the park?
    7·1 answer
  • Wayne purchased 15 pounds of bird seed for $36.75 at Hank's
    12·2 answers
  • Find the sum of the interior angle measures of a pentagon
    14·1 answer
  • This is 7th grade math so pls answer asap<br><br><br>1: v/8=2<br><br>2:16=k/11<br><br>3:18+m=8
    13·1 answer
  • Which expression has a sum equivalent to
    9·1 answer
  • Help! 20 Points! + Brainliest! Which expressions have been simplified correctly? Choose exactly two answers that are correct.
    6·1 answer
  • Drag the tiles to the correct boxes to complete the pairs. simplify the mathematical expressions to determine the product or quo
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!