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Not sure if this works |X+Y|≤|X|+|Y| |X+Y|-|X|-|Y|≤0 0≤ X+Y-X-Y≤ 0 0≤ 0≤ 0

Homework Statement Verify the rule that for two real numbers X and Y then |X+Y|≤|X|+|Y| Homework Equations The Attempt at a Solution 1. When all the variables are positive: |X+Y|=(X+Y) because (X+Y)>0 |X|=X because X>0 |Y|=Y because Y>0 So we got (X+Y)=X+Y 2...

Thank you for the answers, people.

Right. I made a mistake sin(X) or cos(X)= F(X)=Y...No X's. . Can I arrive to that algebraically?

Homework Statement What values of X between 0 and 2 pie radians satisfy each of the following: 1. |sinX|<0.5 2. |cosX|>0.5 Homework Equations The Attempt at a Solution Well the values of X lie between 1. -0.5 < sinX <0.5 2. cosX< -0.5 and cosX>0.5 How do you find the...

Well, because I didn't even think about factoring and finding the zeros. Simple and elegant. X^2- Y^2=0 was given. What I did was X^2=Y^2, then sqrtX^2=sqrtY^2 to "liberate" the variables Y and X. Then I got stuck with the signs the variable X took, what with X being both positive and...

Amazing!

Homework Statement sqrtY^2=sqrtX^2 Solving for Y we get: Y= X and Y= -X Homework Equations The Attempt at a Solution Since both sides of sqrtY^2=sqrtX^2 are equal I thought the equation would solve simply as Y= X. Turns out it has also the second part Y= -X. My questions are since both...