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Elodia [21]
2 years ago
8

Show that √(1-cos A/1+cos A) =cosec A - cot A​

Mathematics
1 answer:
Gennadij [26K]2 years ago
5 0

Hi there!

\sqrt{\frac{1-cosA}{1+cosA}} =

We can begin by multiplying by its conjugate:

\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}}  = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =

Simplify using the identity:

1 - cos^2A = sin^2A

\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =

Take the square root of the expression:

{\frac{sinA}{1+cosA} =

Multiply again by the conjugate to get a SINGLE term in the denominator:

{\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\

Simplify:

{\frac{sinA(1-cosA)}{1-cos^2A} =

Use the above trig identity one more:

{\frac{sinA(1-cosA)}{sin^2A} =

Cancel out sinA:

{\frac{(1-cosA)}{sinA}  =

Split the fraction into two:

{\frac{1}{sinA}   - \frac{cosA}{sinA} =

Recall:

1/sinA = cscA\\\\cosA/sinA = cotA

Simplify:

\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}

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x=5-2y now use this value of x in the second equation...

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Step-by-step explanation:

this is the sample response

4 0
3 years ago
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If the clothing maker bought 500 m2 of this fabric, how much money did he lose? Use 1tepiz=0.625dollar and 0.9144m=1yard.
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1 yard^2 = 0.8361m^2.? 

<span>The solution to the problem is as follows:

So he spent (.625 x 400) = $250.00 per m^2. </span>
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He received (500 / 0.8361) = 598.014592 yard^2 of fabric. 
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He lost (125,000 - 71,761.75) = $53,238.25 on the deal. 

<span>You can rework with the incorrect conversion factor.

I hope my answer has come to your help. God bless and have a nice day ahead!
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