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Virty [35]
3 years ago
6

Prove, cotx -tanx= 2 cot2x

Mathematics
1 answer:
ra1l [238]3 years ago
4 0

Step-by-step explanation:

<em>cotx-</em><em> </em><em>tanx</em><em>=</em><em> </em><em>2cot2x</em>

<em>L.H.S</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>cosx</em><em>/</em><em>sinx-</em><em> </em><em>sinx</em><em>/</em><em>cosx</em><em> </em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>(</em><em>cos</em><em>²</em><em>x-</em><em> </em><em>sin</em><em>²</em><em>x</em><em>)</em><em>/</em><em> </em><em>sinxcosx</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>[</em><em> </em><em>cos</em><em>²</em><em>x-</em><em>(</em><em>1</em><em>-cos</em><em>²</em><em>x</em><em>)</em><em>]</em><em>/</em><em>sinxcosx</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>(</em><em> </em><em>2cos</em><em>²</em><em>x-1</em><em>)</em><em>/</em><em>sinxcosx</em>

<em> </em><em> </em><em> </em><em>2cosx</em><em>/</em><em> </em><em>2sinxcosx</em>

<em> </em><em> </em><em> </em><em>2cot2x</em>

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Simplify this expression:<br> i ^257
Katarina [22]
Okay! 
What is i? 
i = <span>√(-1)

What is i^2? 
i^2 = </span>√(-1) * <span>√(-1) 

Note: Whenever you multiply two square roots with the same numbers you get this: 

</span><span>√(a^2)
</span>
Or in this case: 

√(-1 * -1) = -<span>√(1) = -1
</span>
So, 
i^2 = -1

What does i^3 equal? 
i^3 = √(-1) * √(-1) * √(-1) = 1 * √(-1) = <span>√(-1) which is... -i
</span>
What does i^4 equal? 
i^4 = √(-1) * √(-1) * √(-1) * √(-1) =  √(-1 * -1 * -1 * -1) = 1

After that the cycle does it thing and cycles back. 
So, with this information we can figure out what i^157 equals. 

Knowing long division here helps a lot!
Take 157 and divide it by 4 using long division. If you don't know it, I'll show you how to do it to the best of my abilities. (Refer to the picture. If you have any questions about it then ask. Even if the question is... what does this say?) 

After using long division we see that we get: 
39 with a remainder of 1. 

What that means is: 
(i^4)^39 is what we have. The remainder of 1 means that we have 1 i left. So our answer is i. 

The reason we divided by 4 and not some other term is because i^4 = 1, so it is easy to work with. In this case (i^4)^39 still just equals 1. Which leaves our remainder as our answer. 

So once again the final answer is: 
i

As for i^257. I'll show you the answer, but I won't give the work for this one. I'd recommend you try it out for yourself. 

i^257 = (i^4)^64 * i = i.

I hope that I helped, and if you have any further questions then ask away! 


8 0
3 years ago
,,,,,,,,,,,,,,,,,,,,,,,,,
jonny [76]

Answer:

side

Step-by-step explanation:

if your talking about the dark purple it would be the side but if your talking about the other one it would be front i cant rlly tell by the colors.

i hope this helps:)

8 0
3 years ago
HELP PLEASE ITS DUE TODAY
monitta

Answer:

36 is the shorter length

4 0
2 years ago
Read 2 more answers
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. At a historical la
Alborosie

Answer:

The number of candles will hold 2 candles

And large candle holder will hold 6 candles.

Step-by-step explanation:

Let the number of candles  small candle holder have x

And the number of candles large candle holder have y

So, according to the information given in the question:

17 small candle holders means 17 x

and 2 large candle holders means 2y

using a total of 46 candles means 17x+2y=46     (1)

Similarly, 8 small candle holders and 2 large candle holders, for a total of 28 candles gives:

8x+2y=28      (2)

We will solve equation (1) and (2) by elimination method:

Subtractijng the two equations we get:

9x=18

\Rightarrow x=2

Substitute x=2 in equation(2) we get:8(2)+2y=28

2y=12

\Rightarrow y=6

So, the number of candles will hold 2 candles

And large candle holder will hold 6 candles.

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3 years ago
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NISA [10]

Answer:

afb= 90

cfd= 62

Step-by-step explanation:

4 0
3 years ago
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