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Serggg [28]
3 years ago
11

Verify that -tan2x = (2tanx) / (sec^2x - 2)

Mathematics
1 answer:
sashaice [31]3 years ago
8 0

Answer:

Below.

Step-by-step explanation:

- tan 2x =   -2tanx / (1 - tan^2x)

Using the identity  tan^2x = sec^2x - 1 and substituting for tan^2x:

- tan 2x = -2 tanx / (1 - (sec^2x - 1))

=   2 tanx / ( - 1(sec^2x + 2))

= 2 tan x / (sec^2 x - 2)

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Help question attached multiple choice
Rina8888 [55]

ANSWER

x =  \frac{\pi}{2} , \frac{7\pi}{6} , \frac{3\pi}{2} , \frac{11\pi}{6}

EXPLANATION

The given trigonometric equation is

\cos(x)  + 2 \cos(x)  \sin(x)  = 0

We factor cos(x) to get:

\cos(x) (1 + 2 \sin(x) ) = 0

Apply the zero product property to obtain:

\cos(x)  = 0 \: or \: 1 + 2 \sin(x)  =  0

\cos(x)  = 0 \: or \: \sin(x)  =   -  \frac{1}{2}

Using the unit circle,

\cos(x)  = 0

when

x =  \frac{\pi}{2}

and

x =  \frac{3\pi}{2}

We know

\sin(y)  =  \frac{1}{2}

when

y=  \frac{\pi}{6}

The sine function is negative in the third and fourth quadrants.

x = \pi +  \frac{\pi}{6}  =  \frac{7\pi}{6}

x = 2\pi  -   \frac{\pi}{6}  =  \frac{11\pi}{6}

Hence the solutions are:

x =  \frac{\pi}{2} , \frac{7\pi}{6} , \frac{3\pi}{2} , \frac{11\pi}{6}

6 0
3 years ago
Prove that, in a right triangle with a 15° angle, the altitude to the hypotenuse is one fourth of the hypotenuse.
igomit [66]

Consider the attached figure. If AB has length 1, then BC has length sin(15°) and CD (the altitude of triangle ABC) has length sin(15°)·cos(15°).

By the double angle formula for sin(α), ...

... sin(2α) = 2sin(α)cos(α)

Rearranging, this gives

... sin(α)·cos(α) = sin(2α)/2

We have

... CD = sin(15°)·cos(15°) = sin(2·15°)/2

... CD = sin(30°)/2 = (1/2)/2 = 1/4

That is, the altitude, CD, is 1/4 the hypotenuse, AB, of triangle ABC.

3 0
3 years ago
What is the means-to-MAD ratio of the two data sets, expressed as a decimal to the nearest tenth?
Romashka [77]
To find the mean of a set, add up all of the data points and divide by the number of data points.
For the first set:
(14+18+21+15+17) ÷ 5 = 85 ÷ 5 = 17
For the second set:
(15+17+22+20+16) ÷ 5 = 90 ÷ 5 = 18

To find the MAD (mean absolute deviation) of a set, find the mean of the distances of each data point from the mean.
For the first set:
(3+1+4+2+0) ÷ 5 = 10 ÷ 5 = 2
For the second set:
(3+1+4+2+2) ÷ 5 = 12 ÷ 5 = 2.4

To find the means-to-MAD ratio of a set, divide its mean by its MAD.
For the first set:
17 ÷ 2 = 8.5
For the second set:
18 ÷ 2.4 = 7.5
3 0
3 years ago
Michael drove 210 miles using 9 gallons of gas. At this rate, how many gallons of gas would he need to drive 413 miles?
Mkey [24]

Answer:

210x=3717

x-3717/210

x=7.7 gal1

Step-by-step explanation:


3 0
2 years ago
What is the recursive rule for the sequence?
love history [14]

Answer : option d

4.4, 5.8, 7.2, 8.6, 10, …

First we find the common difference between two terms

5.8 - 4.4 = 1.4

7.2 - 5.8 = 1.4

8.6 - 7.2 = 1.4

10 - 8.6 = 1.4

So common difference is 1.4

To find recursive rule, we add the difference with previous term

Recursive rule is a_n = a_{n-1} + d

a1 is the first term so a1= 4.4

d is the difference = 1.4

So recursive rule is

a_n = a_{n-1} + 1.4, where a1 = 4.4

4 0
2 years ago
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