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mihalych1998 [28]
4 years ago
8

Please help someone, I thought it was 0 but I need two numbers?

Mathematics
1 answer:
Strike441 [17]4 years ago
7 0

Answer:

0 & 0

Step-by-step explanation:

x² + 3 = 3

x² = 0

Root is 0 with multiplicity 2

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Step-by-step explanation:

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Simplify the first trigonometric expression by writing the simplified form in terms of the second expression (1/1-cosx)-(cos/1+c
garik1379 [7]

(\frac{1}{1-cos(x)})-(\frac{cos(x)}{1+cos(x)})

cscx is  1/sinx

maybe they want us to use pythagorean identity

cos^2(x)+sin^2(x)=1

I notice we have 1-cos(x) and 1+cos(x), if we multiply them, we get 1-cos^2(x)

and if we look at the pythagorean identity and minus cos^2(x) from both sides, we get

sin^2(x)=1-cos^2(x)

since csc(x)=\frac{1}{sin(x)}, csc^2(x)=\frac{1}{sin^2(x)}=\frac{1}{1-cos^2(x)}

(recall that (a-b)(a+b)=a²-b²)

match the denomenators of the original fraction

multiply first fraction by \frac{1+cos(x)}{1+cos(x)} and the 2nd by \frac{1-cos(x)}{1-cos(x)}


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

((csc^2(x))(1+cos(x)))-((csc^2(x))(cos(x)-cos^2(x)))=

csc^2(x)+csc^2(x)cos(x)-(csc^2(x)cos(x)-csc^2(x)cos^2(x)=

csc^2(x)+csc^2(x)cos(x)-csc^2(x)cos(x)+csc^2(x)cos^2(x)=

csc^2(x)+csc^2(x)cos^2(x)=

csc^2(x)(1+cos^2(x)), hmm, to get ride of those cos(x)

look to the pythagorean identity again


sin^2(x)+cos^2(x)=1, force one side into form 1+cos^2(x)

1+cos^2(x)=2-sin^2(x), recall that since csc(x)=1/sin(x), sin(x)=1/csc(x) and sin^2(x)=1/(csc^2(x))

1+cos^2(x)=2-\frac{1}{csc^2(x)}

subsituting


csc^2(x)(1+cos^2(x))=

(csc^2(x))(2-\frac{1}{csc^2(x)})= distributing

2csc^2(x)-\frac{csc^2(x)}{csc^2(x)}=

2csc^2(x)-1 is the simplified expression

8 0
3 years ago
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