SOLUTION: 1. csc๐œƒcos๐œƒ/cot๐œƒ=1 2. (sin๐œƒโˆ’cos๐œƒ)^2=1โˆ’sin(2๐œƒ) Hello! For these two problems, I am so lost and don't know what to do or how to solve this. How do verify

Algebra ->  Trigonometry-basics -> SOLUTION: 1. csc๐œƒcos๐œƒ/cot๐œƒ=1 2. (sin๐œƒโˆ’cos๐œƒ)^2=1โˆ’sin(2๐œƒ) Hello! For these two problems, I am so lost and don't know what to do or how to solve this. How do verify      Log On


   



Question 1187011: 1. csc๐œƒcos๐œƒ/cot๐œƒ=1
2. (sin๐œƒโˆ’cos๐œƒ)^2=1โˆ’sin(2๐œƒ)
Hello! For these two problems, I am so lost and don't know what to do or how to solve this. How do verify the identity for both of these?




Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
%28+csc%28theta%29%2Acos%28theta%29%29%2Fcot%28theta%29=1
manipulate left side...........use identity+csc%28theta%29=1%2Fsin%28theta%29
%28+%281%2Fsin%28theta%29%29%2Acos%28theta%29%29%2Fcot%28theta%29
=%28+cos%28theta%29%2Fsin%28theta%29%29%2Fcot%28theta%29................use identity cos%28theta%29%2Fsin%28theta%29=cot%28theta%29
=cot%28theta%29%2Fcot%28theta%29
=1


2,
%28sin%28theta%29-cos%28theta%29%29%5E2=1-sin%282theta%29
manipulate left side
+%28sin%28theta%29-cos%28theta%29%29%5E2......square

=sin%5E2%28theta%29-2sin%28theta%29cos%28theta%29%2Bcos%5E2%28theta%29...........use identity cos%5E2%28theta%29=1-sin%5E2%28theta%29
=sin%5E2%28theta%29-2sin%28theta%29cos%28theta%29%2B1-sin%5E2%28theta%29..........simplify
=-2sin%28theta%29cos%28theta%29%2B1.........rearange
=1-2sin%28theta%29cos%28theta%29+..........................use double angle identity 2sin%28theta%29cos%28theta%29=sin%282theta%29
=1-sin%282theta%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

1. csc๐œƒcos๐œƒ/cot๐œƒ=1
2. (sin๐œƒโˆ’cos๐œƒ)^2=1โˆ’sin(2๐œƒ)
Hello! For these two problems, I am so lost and don't know what to do or how to solve this. How do verify the identity for both of these?
              
------ Substituting
%281%2Fsin+%28theta%29%29+%2A+cos+%28theta%29 รท matrix%281%2C3%2C+cos+%28theta%29%2Fsin+%28theta%29%2C+%22=%22%2C+highlight%281%29%29


highlight_green%28matrix%281%2C3%2C+highlight%281%29%2C+%22=%22%2C+highlight%281%29%29%29