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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 !





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<h3>How to find the area?</h3>

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7 0
1 year ago
There are 5,426 people seated at tables. Each table seats 8 people.
ddd [48]

Answer:

678

2

679

Step-by-step explanation:

Number of people: 5426

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  • Number of full tables= 5426/8= 678.25 so full part is 678

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How many tables are needed for all 5,426 people?​

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What does the y = f(x) represent?
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Step-by-step explanation:

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There are 96 female staff in an office. If the ratio of male staff to female staff is 3:4, find the number of male staff​.
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Answer:60 male staff

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Ok, there are 96 female staff. The ratio of male to female is 3:4. We’re going to use a proportion which looks like this. 3/4 = x/96. X is a variable that takes the place of the male staff since we don’t know what it is. Now, the question is what do we do to get from 4 to 96. So 96/4 = 24, so 4 x 20 = 96. To keep this ratio equivalent whatever you do to the top you have to do to the bottom so 4 x 20 = 96 and 3 x 20 = 60. So there are 60 male staff.

4 0
3 years ago
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