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3 years ago

Sin(a+b) + sin (a-b) = 2 sin a cos b verify the identitiy

Mathematics

1 answer:

Bas_tet [7]3 years ago

6 0

Write out the sum formula for sin
sin(x + y) = sinxcos + sinycosx 

Then expand sin(a + b) + sin(a - b) 
sinacosb + sinbcosa + sinacosb - sinbcosa 
The 2nd and 4th terms cancel and you get 
2sinacosb

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The Johnson twins were born nine years after their older sister. This year, the product of the three siblings ages is exactly 18

KATRIN_1 [288]

Answer: The age of the twins is 10 years.

Step-by-step explanation:

Suppose the age of older sister be x

Let the age of twins sister be x-9, as they are born after 9 years.

Product of their ages be

$x(x-9)(x-9)\\\\=x(x^2-18x+81)\\\\=x^3-18x^2+81x$

Sum of their ages will be

$x+x-9+x-9\\\\=3x-18$

According to question,

$1861+3x-18=x^3-18x^2+81x\\\\x^3-18x^2+81x-3x+18-1861=0\\\\x^3-18x^2+78x-1843=0\\\\x=19$

So, Age of older sister will be 19 years.

Age of the twins will be

$19-9=10\ years$

Hence, the age of the twins is 10 years.

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3 years ago

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noname [10]

Answer:

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Step-by-step explanation:

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2 years ago

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soldier1979 [14.2K]

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Divide 17 by 9
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bezimeni [28]

Answer: (1,3)

Step-by-step explanation:

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