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OLEGan [10]
2 years ago
10

Verify: sec^2x+tan^2x=2sec^2x-1

Mathematics
1 answer:
Jlenok [28]2 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Using the identity

tan²x = sec²x - 1

Consider left side

sec²x + tan²x

= sec²x + sec²x - 1

= 2sec²x - 1

= right side , thus verified

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In a given right triangle, If 0 º < x < 90 º and cos x = √ 3 / 2, then sin x = ?
nordsb [41]

Answer:

  1/2

Step-by-step explanation:

The "Pythagorean relation" between trig functions can be used to find the sine.

<h3>Pythagorean relation</h3>

The relation between sine and cosine is the identity ...

  sin(x)² +cos(x)² = 1

This can be solved for sin(x) in terms of cos(x):

  sin(x) = √(1 -cos(x)²)

<h3>Application</h3>

For the present case, using the given cosine value, we find ...

  sin(x) = √(1 -(√3/2)²) = √(1 -3/4) = √(1/4)

  sin(x) = 1/2

__

<em>Additional comment</em>

The sine and cosine of an angle are the y and x coordinates (respectively) of the corresponding point on the unit circle. The right triangle with these legs will satisfy the Pythagorean theorem with ...

  sin(x)² + cos(x)² = 1 . . . . . . where 1 is the hypotenuse (radius of unit circle)

A calculator can always be used to verify the result.

6 0
1 year ago
Someone Please Help Quickly! Its an Easy Question
Paul [167]

Answer:

y=\frac{2}{3}x-6

Step-by-step explanation:

Use the slope-intercept form:

y=mx+b

m is the slope and b is the y-intercept. Looking at the graph, you can find the y-intercept. The y-intercept is the point where x equals 0:

b=-6

y-intercept=(0,-6)

To find the slope, take any two points from the line:

(6,-2)(3,-4)

Use the slope formula for when you have two points:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}

The rise over run is the change in the y-axis over the change of the x-axis. Insert the appropriate values:

(6(x_{1}),-2(y_{1})\\(3(x_{2}),-4(y_{2})

\frac{-4-(-2)}{3-6}

Simplify parentheses (two negatives makes a positive):

\frac{-4+2}{3-6}

\frac{-2}{-3}

Simplify (two negatives make a positive):

m=\frac{2}{3}

The slope is \frac{2}{3} and the y-intercept is -6. Insert these into the equation:

y=\frac{2}{3}x-6

Finito.

7 0
2 years ago
2X minus one equals five
stepan [7]
2x-1=5
2(3)-1=5
6-1=5
5=5 

x=3
7 0
3 years ago
Read 2 more answers
Is -16/-2 rational or irrational?
mel-nik [20]

Answer:

Totally Rational

Step-by-step explanation:

-16/-2 would give you 8 which is a rational number

<em><u>I hope this helps, dont hesitate to ask for any question.Mark me as brainliest is appreciated.Tq!!</u></em>

4 0
3 years ago
Given that 2x-y÷2y-x=6÷1 find x:y​
Korolek [52]

Answer:

Example Problem

Solve 2x+3=15.

Example Answer

x=6

How to Check Your Answer with Algebra Calculator

First go to the Algebra Calculator main page.

Type the following:

First type the equation 2x+3=15.

Then type the @ symbol.

Then type x=6.

Try it now: 2x+3=15 @ x=6

Step-by-step explanation:

7 0
3 years ago
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