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alexandr1967 [171]
3 years ago
14

Prove that root3 (cosec (20))-sec (20)=4

Mathematics
2 answers:
Tems11 [23]3 years ago
7 0
Root 3 /sin 20 - 1/cos 20

= (root3 cos 20 - sin 20 )/ (sin 20 cos 20)
(multiplying and dividing by 2)
=  2* (root3/2 cos 20 -1/2 sin 20)/ (sin 20 cos 20)

now sin 20 cos 20  = (2 sin 20 cos 20)/2 = (sin 40)/2
and writing root3/2 = sin 60, 1/2 = cos 60

= 2* (sin 60 cos 20 - cos 60 sin 20)/ (sin 40)/2

= 4* (sin (60-20))/sin 40

= 4* (sin 40)/sin 40
=4

Ask if any doubt in any step :)
Mashcka [7]3 years ago
3 0
Hello,

1) Rappels:

all angles are in degree.

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
2sin(a)cos(a)=sin(2a)
sin(a)=cos(90-a)
cos(30)=√3/2
sin(30)=1/2
2)
√3 cos(20)-sin(20)=2(√3/2 cos(20)-1/2 sin(20)
=2*(cos(30) *sin(20)-sin(30) sin(20))=2 cos(30+20)=2 cos(50)

sin(20) cos(20)=1/2 cos(40)=1/2 cos(50)

<span>√3 (cosec (20))-sec (20) = √3 /sin(20)-1/cos(20)
=[√3*cos(20)-sin(20)]/(sin(20)cos(20))
=2 cos(50)/ (1/2cos(50))=4

</span>

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The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

<h3>How to determine the number of real zeros?</h3>

The equation of the function is given as:

f(x) = x^3 + 4x^2 + x - 6

Expand the function

f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6

Reorder the terms

f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6

Factor the expression

f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)

Factor out x -1

f(x) = (x^2 + 5x + 6)(x -1)

Expand

f(x) = (x^2 + 3x + 2x + 6)(x -1)

Factorize

f(x) = [x(x + 3) + 2(x + 3)](x - 1)

Factor out x + 2

f(x) = (x + 3)(x + 2)(x- 1)

The function has been completely factored and it has 3 linear factors

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Two kilograms of bronze costs £7.20<br> What is the cost of 300g of bronze
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We know that
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so
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