All categories

4 years ago

Prove the identity (sin6x)/(1+cos6x)=tan3x.

1 answer:

3 0

Use double angle identity
$sin(2x) = 2 sin x cos x \\ \\ cos(2x) = 2cos^2 x - 1$

We can relate '6x' to '3x' in the same way since 6 is 2*3.
$sin(6x) = 2 sin (3x) cos (3x) \\ \\ cos(6x) = 2cos^2 (3x) - 1$

Now sub into left side of identity. Simplify until it equals right side.
$\frac{2 sin(3x) cos(3x)}{1+(2cos^2 (3x) -1)} = \frac{2 sin(3x) cos(3x)}{2cos^2 (3x) } = \frac{sin(3x)}{cos(3x)} = tan (3x)$

You might be interested in

Please help I'm in desperate need of assistance

ivanzaharov [21]

Answer:

Step-by-step explanation: I think for figure 0 is 7.figure 1 is 9 and the growth is for every increase of the figure number it adds 2 for the tile number.

7 0

3 years ago

A bottling machine in a chemical plant supposed to fill average of 250 ml of acids and the data is approximately normally distri

jasenka [17]

Answer:

Check the explanation

Step-by-step explanation:

(a) P(Type I error) = P( $H_0$ is rejected |

Here we have : µ = 250 and : µ ≠ 250

Here it is given that if 240 < X < 260 then the machine is considered operating satisfactory i.e. is not rejected.

So rejection region is X <= 240 and X >= 260.

Also we know that X follows N( µ , (400/12) ) as population follows N( µ, 400) ; So ( X - µ) / (20 / (12)1/2) follows std. normal distribution.

So, P( is rejected | is true) = P(X <= 240 | µ = 250) + P(X >= 260 | µ = 250)

= P(( X - µ) / (20 / (12)1/2) <=(240 -250)/ (20 / (12)1/2| µ = 250) +

P(( X - µ) / (20 / (12)1/2) >=(260 -250)/ (20 / (12)1/2| µ = 250)

= P(( X - µ) / (20 / (12)1/2) <= -1.7320508076 | µ = 250) + P(( X - µ) / (20 / (12)1/2) >= 1.7320508076 | µ = 250)

And since ( X - µ) / (20 / (12)1/2) follows std. normal distribution. This can be found from Z-tables.

so, = 0.0416 + 0.0416 = 0.0832

(b) P(Type II error) = P( $H_0$ is not rejected | $H_0$ is false) = P(240 < X < 260 | µ ≠ 250)

We have to calculate probability of type II error specifically at µ = 242 so,

= P(240 < X < 260 | µ =242) = P((240 -242)/ (20 / (12)1/2 <= ( X - µ) / (20 / (12)1/2) <= (260 -242)/ (20 / (12)1/2)| µ = 242)

= P(-0.3464101615 <= ( X - µ) / (20 / (12)1/2) <= 3.1176914535 | µ = 242)

And since ( X - µ) / (20 / (12)1/2) follows std. normal distribution. This can be found from Z-tables.

= 0.6346

3 0

3 years ago

What's 1003 in standard form?

Pepsi [2]

<h2>Answer:</h2><h2>1003</h2><h2 /><h2>Hope this helps!!</h2>

6 0

3 years ago

What does splitting a verb mean?

Stels [109]

Splitting a verb represents the meaning to divide lengthwise basically by layers or along a grain.

Explanation:

Splitting a verb represents the meaning as follow :

Word split defines to divide any group into small groups or subgroups.
Splitting a verb explains to divide lengthwise basically in layer form or along a grain.
Splitting a large group into small groups as per the category defined .
For example : Students participates in discussion divided into different groups.
It makes the work easy .
It represent any number or group apart forcibly.

Therefore, splitting a verb represents to divide lengthwise basically layer wise or along a grain.

Learn more about splitting here

brainly.com/question/13188770

#SPJ4

7 0

1 year ago

The point (-3/5,y)in the third quadrant corresponds to angle θ on the unit circle.

anastassius [24]

The given point (-3/5 , y) lies in the third quadrant.
It is also given that the point lies on a unit circle.

For a point (x,y) lying on a unit circle a and y are defined as:

x = cos θ
y = sin θ

So, we can say for the point (-3/5 , y) the value -3/5 is equal to cos θ

sec θ is the reciprocal of cos θ.

So, sec θ = -5/3

$cot\theta= \frac{cos\theta}{sin\theta}$

Using Pythagorean identity we can first find sin θ.

$sin \theta = - \sqrt{1- cos^{2}\theta } \\ \\ 
sin\theta= \sqrt{1-( -\frac{3}{5})^{2} }=- \frac{4}{5}$

Since the point lies in 3rd quadrant, both sin and cos will be negative.

So, now we can write:

$cot\theta= \frac{ \frac{-3}{5} }{ \frac{-4}{5} } \\ \\ 
cot\theta= \frac{3}{4}$

Answers:
sec θ = -5/3
cot θ = 3/4

8 0

3 years ago

Read 2 more answers