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nasty-shy [4]
3 years ago
12

If you could help that would be awesome.

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
6 0

Answer:

2:1

Step-by-step explanation:

4 pencils : 2 pens

simplify...

2 pencils : 1 pen

2:1

Hope this is helpful.

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I need to get the left side to equal the right side. Keeping the right side alone and not changing it.
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<u>To prove the trigonometric equation:</u>

\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)

RHS=(\sin x+\cos x)(1-\sin x \cos x)

We know that \sin^2x +\cos^2x=1, substitute this in place of 1.

       =(\sin x+\cos x)(\sin^2x +\cos^2x-\sin x \cos x)

Multiply each term of the first term with each term of the 2nd term.

       =\sin^3x + \sin x \cos^2x-\sin^2 x \cos x+\cos x \sin^2 x + \cos^3 x-\sin x\cos^2 x

Group like terms together.

       =\sin^3x +( \sin x \cos^2x-\sin x\cos^2 x)+(\cos x \sin^2 x-\sin^2 x \cos x) + \cos^3 x

       =\sin^3x +( 0)+(0) + \cos^3 x

       =\sin^3x + \cos^3 x

       = LHS

RHS = LHS

\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)

Hence proved.

7 0
3 years ago
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