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
saveliy_v [14]
2 years ago
14

Prove that sinxtanx=1/cosx - cosx

Mathematics
1 answer:
maks197457 [2]2 years ago
5 0

Answer:

See below

Step-by-step explanation:

We want to prove that

\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}

Taking the RHS, note

\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}

Remember that

\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)

Therefore,

\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}

Once

\dfrac{\sin(x)}{\cos(x)} = \tan(x)

Then,

\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)

Hence, it is proved

You might be interested in
What is the value of x?
dangina [55]

Answer:

<u>x = 52°</u>

Step-by-step explanation:

The angles add up to 360°.

  • x + 98 + x + 91 + x + 15 = 360
  • 3x + 204 = 360
  • 3x = 156
  • <u>x = 52°</u>
7 0
2 years ago
If the tree cast a shadow of 40 feet, how tall is the tree? A. 30 feet. B.35 ft. C.40 ft. D.45 ft.
Juliette [100K]

Answer:

A)30feet

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
For which function is the ordered pair (5,10) not a solution ?
PilotLPTM [1.2K]

Answer:

D)

Step-by-step explanation:

Because

a)  10 = 2(5) = 10

b) 10 = 5 + 5 = 10

c) 10 = 15 -5 = 10

d) 10 = 5 - 5 = 0  the result is not equivalent

4 0
2 years ago
Read 2 more answers
Anyone help me with this? I will give you brainiest!
kow [346]
3 necklaces were sold and they have got 45 revenue
4 0
3 years ago
Read 2 more answers
A stem-and-leaf plot is made using the following values. Which does NOT correctly represent a line of stem and leaves from the p
melomori [17]

Answer:

7

Step-by-step explanation:

70, 72, 72, 72, 74, 76

There are 6 numbers that have 7 as a 10. There are only 5 ones on the leaf of the stem 7. The 6 is missing.

5 0
2 years ago
Other questions:
  • 2.9n+1.7=3.5+2.3n and the answer is 1... Am I correct???
    9·1 answer
  • Lee sells electronics. He earns a 5% commission on each sale he makes. If lee sells the PS5 for 500, how much does lee make in c
    9·1 answer
  • Ms. Grove likes to bike around a pond nearby to her house. The pond has a radius of 26 feet. If Ms. Grove bikes around the pond
    5·1 answer
  • The booster club sold 36,276 tickets on Friday, 34,012 tickets on Saturday, and 29,879 tickets on Sunday. If you were going to f
    8·2 answers
  • Who is correct?<br> PLease answer ASAP!! pls (:
    13·1 answer
  • Please help 20 points
    15·2 answers
  • Answer this question for me please :(<br> (╹◡╹)<br> 1/3x +5=15
    11·2 answers
  • Which of the following correctly shows the distribution of 4 in the following expression?
    12·1 answer
  • Raju has 2020 one-centimetre square tiles. He
    8·1 answer
  • I REALLY NEED HELP MY GRADES GO IN TONIGHT AND I CANT SOLVE THIS I NEED A REAL ANSWER I WILL CHECK BEFORE GIVING POINTS!!!!!!!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!