2 years ago

Match each device with its advantage.

1 answer:

3 0

<span>A. insulin pump --> ensure accurate doses
B. glucose meter --> provides quick measurement
C. joint implant --> offers pain relief</span>

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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:

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