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
PSYCHO15rus [73]
3 years ago
10

Prove the following identity :Sin α . Cos α . Tan α =  (1 – Cos α)  (1 + Cos α)

Mathematics
2 answers:
lyudmila [28]3 years ago
8 0
<span><u><em>Question</em></u>
Sin α . Cos α . Tan α =  (1 – Cos α)  (1 + Cos α)

<u><em>Answer</em></u>
<u><em>Left side</em> </u> = Sin β . Tan β + Cos β 
               = Sin </span>β . Sin β / Cos β + Cos β
               = Sin² β / Cos β + Cos² β / Cos β
               = 1 / Cos β = Sec β = <u><em>Right side proven</em></u>
Umnica [9.8K]3 years ago
4 0
Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.

sin(a) cos(a) tan(a)

Substitute for the tangent:

[ sin(a) cos(a) ] [ sin(a)/cos(a) ]

Cancel the cos(a) from the top and bottom, and you're left with

[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ]  That's the <u>left side</u>.

Now, work on the right side:

[ 1 - cos(a) ] [ 1 + cos(a) ]

Multiply that all out, using FOIL:

[ 1 + cos(a) - cos(a) - cos²(a) ]

= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.

Do you remember that for any angle, sin²(b) + cos²(b) = 1  ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.

So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .

Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .

They look quite similar. In fact, they're identical. And so the identity is proven.

Whew !





You might be interested in
As a member of a music club, you can order CDs for $14.99 each. The music club also charges $4.99 for each shipment. The express
Dafna1 [17]
Howdy!

using the expression 14.99(n) + 4.99, the total of 3 CDs would cost $49.96.
8 0
3 years ago
Read 2 more answers
It takes 3 hours for two people to weed a garden. How many hour would it take six people to do that task if they were all workin
babunello [35]

Answer:

1 hour

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Pllssss helllppppp award 20 points
madreJ [45]

Answer:11

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend
sveta [45]

Answer:

12 diffence

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A new motorboat costs $6000. The value of the boat decreases by 15% each year. What is the value of the boat after 3 years?
Elodia [21]

Answer:

 The value of the boat after 3 years is \$3,684.75  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

V=P(1-r)^{x}  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

P=\$6,000\\r=15\%=15/100=0.15\\x=3\ years

substitute

V=6,000(1-0.15)^{3}  

V=6,000(0.85)^{3}

V=\$3,684.75  

6 0
3 years ago
Other questions:
  • I found a place that would give me a 20% discount if spend over $50. My bill is $75. what is my final bill after the savings
    7·1 answer
  • Please tell me if my answer is right.. The question- Approximately how many gigabytes (GB) of new data will be produced in 2012?
    13·1 answer
  • Joel uses a claw hammer to remove a nail from a wall. He applies a force of 40 newtons on the hammer. The hammer applies a force
    8·2 answers
  • Can someone please help with number 12? Will give brainliest to best answer!
    15·2 answers
  • Please solve the following problem
    10·1 answer
  • Help I can't figure out theese pleas se help
    9·1 answer
  • Find g(f(-1)).<br> g(f(-1)) =<br> DONE
    12·1 answer
  • Answer? plsssssssssssssss
    8·2 answers
  • PLS PLS HELP ILL MARK U BRAINLIEST
    13·2 answers
  • Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it. You randomly ask 20 Greensboro voter
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!