Question

what are these about ? Can anyone explain to me this part? PLEASE :(

Answer 1

It sets a condition: When thex and y units add to 90, tanx= recoprocal of tany

The chart gives the values of trig. function when at certain degrees. When we looks ar tanΘ, we are given the x and y values, becuase tanΘ= y/x
    

Answer 2

The answer is 45 degrees

The reciprocal of any function is 1 over the function 

for example, the reciprocal of $sin\ x \ \ \ is \ \ \ \frac{1}{sin \ x}$

So
if x + y = 90 

The value of x and y should be the same bcz

$tan \ x = \frac{1}{tan \ y}$  means that the function is reciprocal and the measure of their angles (x and y) have to be the same

45 + 45 = 90

x = 45
y = 45