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lana66690 [7]
3 years ago
12

Prove this trigonometric equation; - tan^2x + sec^2x = 1,

Mathematics
1 answer:
alekssr [168]3 years ago
3 0
Hey there :)

- tan²x + sec²x = 1    or    1 + tan²x = sec²x

sin²x + cos²x = 1 
Divide the whole by cos²x

\frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x}

\frac{sinx}{cosx} = tanx so \frac{sin^2x}{cos^2x} = tan^2x
and
\frac{1}{cosx} = secx so \frac{1}{cos^2x} = sec^2x

Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}

1 = - tan²x = sec²x or sec²x - tanx = 1

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One family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park. Another family spends $146 on 3 adult ticket
AnnZ [28]
3x + 2y = $134
2x + 3y = $146

Using elimination to solve for x

9x +6y = 3*134 Multiplying 1st equation by 3

-4x -6y = -2*146 | Multiplying 2nd equation by -2



5x = 3*134 - 2*146

5x = $110

x = $22, the cost of the youth ticket

Put x= 22 Into An Equation Then Solve For y

3(22)+2y= 134
66+ 2y=134
Subtract 66
2y=68
Y= 34

CHECKING Answer ($34 being the cost of the adult ticket) y = (134-3*22)/2

3*$22 + 2*$34 = $66 + $68 = $134
8 0
3 years ago
Jalen has a scale model of a train. 2 centimeters in the
mariarad [96]

Answer:

15.3feet

Step-by-step explanation:

Given the scale model of a train as;

2cm = 3feet

We are to find the height of real train of height 10.2cm, we can write;

10.2cm = x

Divide both expressions

2/10.2 = 3/x

2x = 3×10.2

2x = 30.6

x= 15.3

Hence the height if the real train is 15.3feet

8 0
3 years ago
Elijah is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 2 points. What woul
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Answer:

84 points

y= 100-2x where y= total score (0 through 100) and x= # of questions wrong (0 through 50)

Step-by-step explanation:

100- 2(8) = y

100-16 = y

84=y

Since each question (x) is worth two points (2) we have to multiply each wrong question by two (2x). And then since we're deducting point from the possible points (100) we have to subtract (100-2x)

3 0
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pickupchik [31]

Answer: y= -7   y= -5   y= -3   y= -1

Step-by-step explanation:

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2 years ago
I need help im failing
aleksley [76]

Answer:

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Step-by-step explanation:

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