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3 years ago

Prove csc(pi/2 -x) = sec x

Mathematics

1 answer:

kifflom [539]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Using the trigonometric identities

csc x = $\frac{1}{sinx}$ and sec x = $\frac{1}{cosx}$

Note that sin( $\frac{\pi }{2}$ - x) = cos x

Hence

csc( $\frac{\pi }{2}$ - x)

= $\frac{1}{sin(\frac{\pi }{2}-x) }$

= $\frac{1}{cosx}$

= sec x = right side ⇒ proven

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Calculate the distance between the points H=(3,-1) and E=(8,-5) in the coordinate plane. Give an exact answer (not a decimal app

tester [92]

Answer: $\sqrt{41}$

===========================================

Work Shown:

Use the distance formula.

$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-1-(-5))^2+(3-8)^2}\\\\d = \sqrt{(-1+5)^2+(3-8)^2}\\\\d = \sqrt{(4)^2+(-5)^2}\\\\d = \sqrt{16+25}\\\\d = \sqrt{41}\\\\$

Or you could use the pythagorean theorem, which is how the distance formula is set up.

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2 years ago

A square part of side 20 meters has a footpath along the boundary of width 10 meters . Find the area of path

qaws [65]

Answer:

Answer: 84 meters squared. (i.e. 84m^2).

Step-by-step explanation:

Area of the path = total area of path and plot - plot area only

First, let’s find the area of the plot:

20m x 20m = 400m^2

The path is 1m wide and runs all the way around, so, it describes an ‘outer square’ of 22m x 22m (2 x 1m larger because there are 1m of the path on each side).

The area of this ‘outer square’ is equivalent to the ‘total area of path and plot’

22m x 22m = 484m^2

So:

Area of the path = total area of path and plot - plot area only

= 484 - 400 = 84m^2

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2 years ago

Find three consecutive natural numbers if the square of the smallest number is 65 less than the product of the two remaining num

garri49 [273]

Answer:

21 22 23

Step-by-step explanation:

6 0

2 years ago

Please answer and show work!!!!!!!!!

bixtya [17]

⚘Kindly refer to the attachments for complete solutions!!~

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1 year ago

Someone help find surface area of a right rectangular prism

Bond [772]

Answer:

51 square units

Step-by-step explanation:

First you act like each side is it’s separate rectangle.

Then you would multiply 2 and 4 to get 8, the area of one of the sides. Then you would multiply 2 and 2.5 to get 5, the area of another side. Then 2.5 times 5 to get 12.5, the last side. Now sense every side has a side the same size of itself you would take each answer and multiply it by to to get 8x2=16, 5x2=10, and 12.5x2= 25. You would add together 16, 10, and 25 to get 51 square units, the surface area.

3 0

2 years ago