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2 years ago

Prove that 1/sin^2A -1/tan^2A= 1

Mathematics

1 answer:

Vika [28.1K]2 years ago

4 0

Answer:

Step-by-step explanation:

$LHS =\dfrac{1}{Sin^{2} \ A }-\dfrac{1}{Tan^{2} \ A }\\\\\\ = \dfrac{1}{sin^{2} \ A}- \dfrac{1}{\dfrac{Sin^{2} \ A}{Cos^{2} \ A}}\\\\\\= \dfrac{1}{sin^{2} \ A } - \dfrac{Cos^{2} \ A}{Sin^{2} \ A}\\\\\\= \dfrac{1-Cos^{2} \ A}{Sin^{2} \ A}\\\\\\= \dfrac{Sin^{2} \ A}{Sin^{2} \ A}\\\\\\= 1 = \ RHS$

Hint: 1 - Cos² A = Sin² A

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torisob [31]

Answer : 6 is opposite of 1

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3 years ago

the midpoint is AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.

cestrela7 [59]

Answer:

The required points of the given line segment are ( - 1, - 5 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( $x_{1}, y_{1}$ ) and ( $x_{2}, y_{2}$ )then the mid points M are-

M = ( $\frac{ x_{1} + x_{2} }{2}$ , $\frac{ y_{1} + y_{2} }{2}$ )

Here,

Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -

then by the midpoint formula M are-

( 3, - 2 ) = ( $\frac{ 7 + x}{2}$ , $\frac{ - 9 + y}{2}$ )

On comparing x coordinate and y coordinate -

We get,

( $\frac{ 7 + x}{2}$ = 3 , $\frac{ - 9 + y}{2}$ = - 2)

( 7 + x = 6, - 9 + y = - 4 )

( x = 6 - 7, y = - 4 + 9 )

( x = - 1, y = -5 )

Hence the required points A are ( - 1, - 5 ).

We can also verify by putting these points into Midpoint formula.

8 0

3 years ago

Alison bought a video game for $35, which was 35% off the original price. What was the original

Jlenok [28]

Answer: the answer to your question is $57.75

Step-by-step explanation: so first you have to realize that if you have something that is 35 percent off then you have .65 of that thing so you multiply 35 by .65 then you get 22.75 then you add that to 35 for your answer.

3 0

3 years ago

Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year.

Drupady [299]

Answer:

Range = 13

Variance = 10.22

Standard deviation = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

Step-by-step explanation:

We are given the number of hurricanes that occurred in each year in a certain region.

8 9 8 7 9 15 5 6 8 4 12 7 8 2

Range:

The range of the data set is found by

Range = Maximum value - minimum value

The maximum value in the data set is 15

The minimum value in the data set is 2

Range = 15 - 2

Range = 13

Variance:

To find the variance, first compute the mean of the data set.

Mean = Sum/n

Mean = (8+9+8+7+9+15+5+6+8+4+12+7+8+2)/14

Mean = 108/14

Mean = 7.714

The variance is given by

σ² = (x - mean)²/(n - 1)

σ² = (8 - 7.714)² + (9 - 7.714)²+ (8 - 7.714)² + (7 - 7.714)² + (9 - 7.714)² + (15 - 7.714)² + (5 - 7.714)² + (6 - 7.714)² + (8 - 7.714)² + (4 - 7.714)² + (12 - 7.714)² + (7 - 7.714)² + (8 - 7.714)² + (2 - 7.714)²/(14 - 1)

σ² = 10.22

Standard deviation:

The standard deviation of the data set is given by

σ² = √σ

σ² = √10.22

σ² = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

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3 years ago

To join a Yoga Class at The Yoga Emporium the cost is

QveST [7]

The answer is 5x+50=y
Because you have to pay 50 dollars to get a lesson you have to pay it plus the number of lessons multiplied by the price.

3 0

2 years ago

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