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Galina-37 [17]
2 years ago
15

Cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.

Mathematics
1 answer:
umka21 [38]2 years ago
8 0

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

  tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

  tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

  tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

  tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

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Answer:

We conclude that the average height of hobbit is taller than Yoda.

Step-by-step explanation:

We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.

From a sample of 7 hobbits, you find their mean height \bar X = 80 cm with standard deviation s = 10.8 cm.

<u><em /></u>

<u><em>Let </em></u>\mu<u><em> = average height of hobbit.</em></u>

So, Null Hypothesis, H_0 : \mu \leq 66 cm      {means that the average height of hobbit is shorter than or equal to Yoda}

Alternate Hypothesis, H_A : \mu > 66 cm      {means that the average height of hobbit is taller than Yoda}

The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about population standard deviation;

                     T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}  ~ t_n_-_1

where, \bar X = sample mean height = 80 cm

             s = sample standard deviation = 10.8 cm

             n = sample of hobbits = 7

So, <u><em>test statistics</em></u>  =  \frac{80-66}{\frac{10.8}{\sqrt{7}}}  ~ t_6

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The value of t test statistics is 3.429.

<em>Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>

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Therefore, we conclude that the average height of hobbit is taller than Yoda.

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3 years ago
Conference A and conference B each have 10 football teams. The table shows the number of football games that each team in the tw
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Answer with explanation:

1.Mean of a Data set

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=\frac{10+9+11+8+10+12+2+7+8+0+12+10+8+11+3+12+6+7+4+3}{20}\\\\=\frac{153}{20}\\\\=7.65

2. Range = Maximum value in two conferences - Minimum value in two conference

= 12 - 0

=12

The mean number of wins for teams from the two conferences is 7.65.

The range in wins is  12.

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Given:

The graph of a line.

To find:

The point-slope form of the given line.

Solution:

From the given graph it is clear that the line passes through the point (1,5) and (0,-1). So, the slope of the line is:

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{-1-5}{0-1}

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The slope of the line is 6 and it passes through the point (1,5). So, the point slope form of the line is:

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Therefore, the point-slope form is y-5=6(x-1), slope is 6 and the point is (1,5).

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Answer:

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Step-by-step explanation:

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We have a=3f and b=5g here.

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The ? is 15.

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2 years ago
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