Verify the identity algebraically:
cot(a) / (csc(a)-1) = csc(a) + 1/cot(a)

1

+

cot

2

x

=

csc

2

x

.

Step-by-step explanation:

"Remember that

1

+

cot

2

x

=

csc

2

x

.

Explanation:

cot

x

csc

x

−

1

=

csc

x

+

1

cot

x

Remember that

1

+

cot

2

x

=

csc

2

x

. This becomes useful if we multiply the terms with

csc

x

to get them squared:

cot

x

csc

x

−

1

(

csc

x

+

1

csc

x

+

1

)

=

csc

x

+

1

cot

x

cot

x

csc

x

+

cot

x

csc

2

x

−

1

=

csc

x

+

1

cot

x

We can now use

csc

2

x

−

1

=

cot

2

x

cot

x

csc

x

+

cot

x

cot

2

x

=

csc

x

+

1

cot

x

csc

x

+

1

cot

x

=

csc

x

+

1

cot

x"

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

can i see the following ?

step-by-step explanation: