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Evgen [1.6K]
4 years ago
9

I don't understand parabola's ?

Mathematics
2 answers:
Ksivusya [100]4 years ago
6 0
<span>a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.</span>
vovikov84 [41]4 years ago
4 0
Well, according to the dictionary, a parabola is: "<span>a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape."
or "</span><span>The </span>parabola<span> is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the </span>parabola<span> up the middle) is called the "axis of symmetry"".</span><span>
Hope this helps~!
~{Dunsforhands}</span>
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Answer:

see explanation

Step-by-step explanation:

(4)

consider the left side

factor the numerator

cosx - cos³x = cosx(1 - cos²x)

\frac{cosx(1-cos^2x)}{sinx}[/tex = [tex]\frac{cosxsin^2x}{sinx}

cancel sinx on numerator/denominator

= cosxsinx =right side ⇒ verified

(5)

Consider the left side

expand the factors

(1 + cotΘ)² + (1 - cotΘ)²

= 1 + 2cotΘ + cot²Θ + 1 - 2cotΘ + cot²Θ

= 2 + 2cot²Θ

= 2(1 + cot²Θ) ← 1 + cot²Θ = cosec²Θ

= 2cosec²Θ = right side ⇒ verified

(6)

Consider the left side

the denominator simplifies to

cosxtanx = cosx × \frac{sinx}{cosx} = sinx

\frac{sin^2x(secx+cosecx)}{sinx}

= sinx( \frac{1}{cosx} + \frac{1}{sinx})

= \frac{sinx}{cosx} + \frac{sinx}{sinx}

= tanx + 1 = right side ⇒ verified











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