tan (A-B) + tan (B-C) + tan (C-A)=0
tan (A-B) + tan (B-C) - tan (A-C)=0
tan (A-B) + tan (B-C) = tan (A-C)
(A-B) + (B-C) = A-C
So we can solve
tan (A-B) + tan (B-C) = tan (A-C)
by first solving
tan x + tan y = tan (x+y)
and then substituting x = A-B and y = B-C.
tan (x+y) = (tan x + tan y)/(1 - tan x tan y)
So tan x + tan y = (tan x + tan y)/(1 - tan x tan y)
(tan x + tan y)tan x tan y = 0
So, tan x = 0 or tan y = 0 or tan x = - tan y
tan(A-B) = 0 or tan(B-C) = 0 or tan(A-B) = - tan(B-C)
tan(A-B) = 0 or tan(B-C) = 0 or tan(A-B) = tan(C-B)
A, B and C are all angles of a triangle, so are all in the range (0, pi).
So A-B and B-C are in the range (- pi, pi).
At this point I sketched a graph of y = tan x (- pi < x < pi)
By inspection I can see that:
A-B = 0 or B-C = 0 or A-B = C-B or A-B = C-B +/- pi
A = B or B = C or A = C or A = C +/- pi
But A and C are both in the range (0, pi) so A = C +/- pi has no solution
So A = B or B = C or A = C
A triangle ABC has the property that tan (A-B) + tan (B-C) + tan (C-A)=0 if and only if it is isosceles (or equilateral).
2 plus 3 equals 5 7 plus 2 equals 9 6 plus 9 equals 15 8 plus 4 equals 12 9 plus 7 equals 16 Am I missing something here? Probably. You say 2+3=5, but the question clearly states 2+3=10. Why would it say that? Suppose you had only one hand. You count 1,2,3,4,5,10,11,12. That last doesn't mean "twelve" as we know it, Jim. It means one hand (5), plus 2 spare ones. We could say: if 2+3=10, 5+2=12.
The formula is A2 + B2=C2. Say if 102 +102=202.The hypotenuse is 202.So 102 +102=200.And 202=200. the triangle is a right triangle. It equals the hypotenuse.
there is a multitude of answers to that. Let's say Y equals 2 and X equals 5. So -5 plus 3(2)= 1
It is a straight line with gradient -A/B and intercept C/B.
The telephone keypad is the clue to the answer.7ai64364 2a87 a6e 3647raining cats and dogs
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.Here are some examples that I hope can help you throughExample 1:Let's say that Triangle ABC has these measures:Let's also say that Triangle DEF has the measures:Then you know that angle C is congruent to angle F through CPCTC.Example 2:Let's say that Triangle ABC has these measures:Let's also say that Triangle DEF has the measures:Then you know that side CA is congruent to side FD through CPCTC.Example 3:Let's say that Triangle ABC has these measures:Let's also say that Triangle DEF has these measures:Then you know that side AC is congruent to DF through CPCTC.You also know that angle C is congruent to angle F through CPCTC.You also know that angle A is congruent to angle D through CPCTC.
2 plus 3 equals 5 7 plus 2 equals 9 6 plus 9 equals 15 8 plus 4 equals 12 9 plus 7 equals 16 Am I missing something here? Probably. You say 2+3=5, but the question clearly states 2+3=10. Why would it say that? Suppose you had only one hand. You count 1,2,3,4,5,10,11,12. That last doesn't mean "twelve" as we know it, Jim. It means one hand (5), plus 2 spare ones. We could say: if 2+3=10, 5+2=12.
The formula is A2 + B2=C2. Say if 102 +102=202.The hypotenuse is 202.So 102 +102=200.And 202=200. the triangle is a right triangle. It equals the hypotenuse.
there is a multitude of answers to that. Let's say Y equals 2 and X equals 5. So -5 plus 3(2)= 1
vier plus eins ist funf
It is a straight line with gradient -A/B and intercept C/B.
because it does say its Twenty OnE
5 + 5 = 10
Say It - ABC song - was created in 1992-01.
The telephone keypad is the clue to the answer.7ai64364 2a87 a6e 3647raining cats and dogs
Yes, but on ly if you don't say "equals 10 " at the end.
Get two slaves. Give one equation to each slave. Say, "Go!"