SOLUTION: Prove that the given statement is an identity. 1)(tan x - cot x)/ (tan x+cot x) = 2sin^2 x - 1

Algebra ->  Trigonometry-basics -> SOLUTION: Prove that the given statement is an identity. 1)(tan x - cot x)/ (tan x+cot x) = 2sin^2 x - 1      Log On


   

Question 439286: Prove that the given statement is an identity.
1)(tan x - cot x)/ (tan x+cot x) = 2sin^2 x - 1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28tan%28x%29+-cot%28+x%29%29%2F%28tan+x%2Bcot+x%29=2(sin^2)x



use identities:
sin%28x%29+%2F+cos%28x%29+
cot%28x%29+=+cos%28x%29%2F+sin%28x%29
prove that left side is equal to right side:
%28tanx+-cotx%29%2F%28tanx%2Bcot+x%29 =2sin^2x -1

%28sinx%2Fcosx+-cosx%2Fsinx%29%2F%28sinx%2Fcosx%2Bcosx%2Fsinx%29 = 2sin^2 x - 1



= 2sin^2 x - 1


= 2sin^2 x - 1

%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29= 2sin^2 x - 1...notice that both nominator and denominator have sin and coc squared

%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F1= 2sin^2 x - 1

replace cos^2x with 1-sin%5E2%28x%29

sin%5E2%28x%29-%281-sin%5E2%28x%29%29= 2sin^2 x - 1

sin%5E2%28x%29-1%2Bsin%5E2%28x%29= 2sin^2 x - 1
2sin%5E2%28x%29-1= 2sin^2 x - 1