SOLUTION: Proof: 2-(sin θ -cos θ )^2= (sinθ+cosθ)^2 THanks

Algebra ->  Trigonometry-basics -> SOLUTION: Proof: 2-(sin θ -cos θ )^2= (sinθ+cosθ)^2 THanks      Log On


   

Question 934716: Proof:
2-(sin θ -cos θ )^2= (sinθ+cosθ)^2
THanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2-%28sin+%28theta%29+-cos%28theta%29+%29%5E2=%28sin%28theta%29%2Bcos%28theta%29%29%5E2
proof:
2-%28sin+%28theta%29+-cos%28theta%29+%29%5E2=
2-%28sin%5E2+%28theta%29+-2sin%28theta%29cos%28theta%29+%2Bcos%5E2%28theta%29%29=
2-sin%5E2+%28theta%29+%2B2sin%28theta%29cos%28theta%29+-cos%5E2%28theta%29%29=
2%2B2sin%28theta%29cos%28theta%29-sin%5E2+%28theta%29++-cos%5E2%28theta%29=
2%2B2sin%28theta%29cos%28theta%29-%28sin%5E2+%28theta%29++%2Bcos%5E2%28theta%29%29=...............we know cos%5E2%28theta%29+%2B+sin%5E2%28theta%29=+1
2%2B2sin%28theta%29cos%28theta%29-1=
1%2B2sin%28theta%29cos%28theta%29= since cos%5E2%28theta%29+%2B+sin%5E2%28theta%29=+1
cos%5E2%28theta%29+%2B+sin%5E2%28theta%29%2B2sin%28theta%29cos%28theta%29=
+sin%5E2%28theta%29%2B2sin%28theta%29cos%28theta%29%2Bcos%5E2%28theta%29=
= %28sin%28theta%29%2Bcos%28theta%29%29%5E2