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3 years ago

HELP PLEASE ALGEBRA!!!!

Mathematics

1 answer:

Ksivusya [100]3 years ago

3 0

Answer:

Step-by-step explanation:

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True or false. Tan^2 x = 1 - cos2x/ 1 + cos 2x

koban [17]

<u>ANSWER</u>

True

<u>EXPLANATION</u>

The given trigonometric equation is

$\tan^{2} (x) = \frac{1 - \cos(2x) }{1 + \cos(2x) }$

Recall the double angle identity:

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

We apply this identity to obtain:

$\tan^{2} (x) = \frac{1 - (\cos^{2} x - \sin^{2}x) }{1 + (\cos^{2} x - \sin^{2}x) }$

We maintain the LHS and simplify the RHS to see whether they are equal.

Expand the parenthesis

$\tan^{2} (x) = \frac{1 - \cos^{2} x + \sin^{2}x }{1 + \cos^{2} x - \sin^{2}x}$

$\implies\tan^{2} (x) = \frac{1 - \cos^{2} x + \sin^{2}x }{1 - \sin^{2}x + \cos^{2} x }$

Recall that:

$1 - \sin^{2}x = \cos^{2}x$

$1 - \cos^{2}x = \sin^{2}x$

We apply these identities to get:

$\implies\tan^{2} (x) = \frac{\sin^{2}x + \sin^{2}x }{\cos^{2} x + \cos^{2} x }$

$\implies\tan^{2} (x) = \frac{2\sin^{2}x }{ 2\cos^{2} x }$

$\implies\tan^{2} (x) = \frac{\sin^{2}x }{ \cos^{2} x }$

$\implies \tan^{2} (x) =( \frac{\sin x }{ \cos x })^{2}$

Also

$\frac{\sin x }{ \cos x } = \tan(x)$

$\implies \tan^{2} (x) =( \tan x )^{2}$

$\implies \tan^{2} (x) =\tan^{2} (x)$

Therefore the correct answer is True

5 0

4 years ago

two jets leave an airport at the same time in opposite directions. the first jet is traveling at 323 mph and the other at 347 mp

skelet666 [1.2K]

Remark

This may be a little confusing, but because they are travelling in opposite directions, the distances add when you want to get how far apart they are.

d1 + d2 = 1541

Equation

Let the time this happens = t

d1 = 323*t

d2 = 347*t

323*t + 347*t = 1541 Combine like terms on the left.

670t = 1541 Divide by 670

t = 1541/670

t = 2.3 hours pass before the distance of 1541 miles are between the two planes. You might need the answer to be 2 hours 18 minutes.

4 0

3 years ago

Question 20 of 25

Alex777 [14]

Answer: D

Step-by-step explanation:

A P E X

4 0

3 years ago

HELP PLEASE! BRAINLIEST

V125BC [204]

Since AED forms a straight line, all involved angles sum to 180°. Therefore AEB + BED = 180. Also, since EC bisects BED, BEC = CED, and BED = 2× CED. Now to substitute the first equation:
AEB + BED = 180
AEB + 2×CED = 180
11x-12 + 2(4x+1) = 180
11x-12+8x+2 = 180
19x-10 = 180
19x-10+10 = 180+10
19x = 190
x = 10
So what is m<AEC?? It is the sum of AEB + BEC, and since BEC = CED we can say that:
AEC = AEB + CED
AEC = 11x-12 + 4x+1 = 15x-11 = 15(10)-11 = 150-11
m<AEC = 139°

3 0

4 years ago

Estimate the circumference of the circle to the nearest hundredth. Use π = 3.14

nekit [7.7K]

The formula for the circumference of a circle is 2πr. r stands for the radius ehich is 1/2 of the diameter (the length from one edge of the circle to another on the inside of the circle). If you are estimating then you will want to change π to three and put that in for pie in the original equation.

6 0

3 years ago