Answer:
See proof below
Step-by-step explanation
cot^2(x) - csc^2(x) = -1
In trigonometry identity
cot^2x = cos²x/sin²x
Csc²x = 1/sin²x
Substitute into the original expression
cos²x/sin²x - 1/sin²x
Find the LCM
(Cos²x-1)/sin²x .... *
Recall that sin²x+cos²x = 1
Sin²x = 1-cos²x
-sin²x = -1+cos²x
-sin²x = cos²x-1 .... **
Substitute ** into *
(Cos²x-1)/sin²x
-sin²x/sin²x
= -1 (RHS)
Therefore cot^2(x) - csc^2(x) = -1 (Proved!)
I had the same math and it’s pretty complicated
Answer:
Rule: If it ends with a 0, 2, 4, 6, or 8 it is divisible by 2
for divisibility rule of 3 add all digits if it is a part of the table of 3 it is divisible
Rule: If the last two digits are a multiple of 4
(or if the last two digits are 00) for 4
Rule: If the last two digits are a multiple of 4
(or if the last two digits are 00) for 5
Rule: If it is divisible by 2 and by 3 for 6
Rule: If the sum of the digits are a multiple of 9 for 9
Rule: If the last digit is 0 for 10
I think it would be obtuse, triangle, and a cute
Let g = original # of girls at the assembly.
Let w = # of boys at the assembly.
Equation of ratios:
w 3 boys
------- = ---- = --------------------------------------------
g-12 4 girls after 12 have left assembly
4w + 36
Cross-mult., 4w = 3g - 36, so 4w + 36 = 3g, and g = --------------- (answer)
4
This is "original # of girls at the assembly in terms of w, the # of boys at the assembly."