2 years ago

Match each chronic disease with one of its risk factors.

2 answers:

7 0

Correct answer
Diabetes risk factor is family history because its genetic disease
Stroke risk factor is smoking tobacco which causes arteriosclerosis
Allergies risk factor is air quality because most allergens are found in the air such as dust.

Savatey [412]2 years ago

3 0

allergies-air quality

diabetes-family history

stroke-tobacco use

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Prove sinA*cos2A=1/4sin4A*secA<br>

kolezko [41]

Answer:

The prove is below

Explanation:

From trigonometric identities:

$cos2A=cos(A+A)=cos^2A-sin^2A\\sin2A=sin(A+A)=2sinAcosA\\sin4A=sin(2A+2A)=2sin2Acos2A=2(2sinAcosA)(cos^2A-sin^2A)=4sinAcos^3A-4cosAsin^3A\\secA=\frac{1}{cosA}$

Therefore:

$\frac{1}{4}sin4AsecA = \frac{1}{4}( 4sinAcos^3A-4cosAsin^3A)\frac{1}{cosA}\\= sinAcos^3A-cosAsin^3A(\frac{1}{cosA} )\\=sinAcos^2-sin^3A\\=sinA(cos^2A-sin^2A)\\But\ cos^2A-sin^2A=cos2A\\Therefore:sinA(cos^2A-sin^2A)=sinAcos2A\\\frac{1}{4}sin^4Acos2A=sinAcos2A$