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saveliy_v [14]
2 years ago
14

Prove that sinxtanx=1/cosx - cosx

Mathematics
1 answer:
maks197457 [2]2 years ago
5 0

Answer:

See below

Step-by-step explanation:

We want to prove that

\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}

Taking the RHS, note

\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}

Remember that

\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)

Therefore,

\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}

Once

\dfrac{\sin(x)}{\cos(x)} = \tan(x)

Then,

\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)

Hence, it is proved

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Molodets [167]

Answer:

8409 es 8×10³ es 8 4×10² es 4 0×10¹ es 4 9×10⁰ es 9

7 0
2 years ago
Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value
algol [13]

Answer:

Minimum value of function C=x+10y is 63 occurs at point (3,6).

Step-by-step explanation:

To minimize :

                                   C=x+10y

Subject to constraints:

                                   x\leq 3---(1)\\y\leq 9---(2)\\x+y\geq 9----(3)\\x\geq 0\\y\geq 0

Eq (1) is in blue in figure attached and region satisfying (1) is on left of blue line

Eq (2) is in green in figure attached and region satisfying (2) is below the green line

Considering x+y\geq 9, corresponding coordinates point to draw line are (0,9) and (9,0).

Eq (3) makes line in orange in figure attached and region satisfying (3) is above the orange line

Feasible region is in triangle ABC with common points A(0,9), B(3,9) and C(3,6)

Now calculate the value of function to be minimized at each of these points.

                                    C=x+10y

at A(0,9)

                                     C=0+10(9)\\C=90

at B(3,9)

                                     C=3+10(9)\\C=93

at C(3,6)

                                     C=3+10(6)\\C=63

Minimum value of function C=x+10y is 63 occurs at point C (3,6).

3 0
3 years ago
There are several ways you might think you could enter numbers in WebAssign, that would not be interpreted as numbers. N.B. Ther
Vikki [24]

Answer:

a) 1.56e^{-9}

b) -4.99

d) 1.9435

Step-by-step explanation:

We are given certain rule to identify number. We have to identify from the entries that can be interpreted as numbers.

a) 1.56e-9

This a number as there are no spaces, no comma, no units.

b) -4.99

This a number as there are no spaces, no comma, no units.

c) 40O0

This is not a number as 0 is substituted by O.

d) 1.9435

This a number as there are no spaces, no comma, no units.

e) 1.56 e-9

This is not a number as it contains a space.

f) $2.59

This is not a number as it contains a dollar sign.

g) 3.25E4

This is not a number as it contains alphabet.

h) 5,000

This is not a number as there is a comma in the given.

i) 1.23 inches

This is not a number as it contains a unit.

5 0
3 years ago
What is the final answer for 6x-6-7x=-13/2
olya-2409 [2.1K]
6x - 6 - 7x = -13/2

Multiply both sides by 2:
12x - 12 - 14x = -13

Simplify:
-2x - 12 = -13

Add 12 to both sides:
-2x = -1

Divide both sides by 2:
-x = -1

Change to a positive value of x:
x = 1

6 0
3 years ago
Math question plz help me
Minchanka [31]

Answer:

The required equation of the line is:

y=\frac{1}{4}x-1

Step-by-step explanation:

Given the equation

y=-4x+3

comparing the equation with the slope-intercept form

y=mx+b

Here,

  • m is the slope
  • y is the intercept

so the slope of the line is  -4.

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be: 1/4

Therefore, the point-slope form of the equation of the perpendicular line that also intersects the point (8, 1) is:

y-y_1=m\left(x-x_1\right)

y-1=\frac{1}{4}\left(x-8\right)

add 1 to both sides

y-1+1=\frac{1}{4}\left(x-8\right)+1

y=\frac{1}{4}x-1

8 0
3 years ago
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