Prove the Identity (1-cos2x)(1+cot2x)=1?

3 ⤊

both numbers 2 are exponents

2007-11-21 09:41:41 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

(1-cos²x)(1+cot²x) =
= sin²x (1 + cos²x / sin²x) =
= sin²x + cos²x = 1

2007-11-21 09:54:41 · answer #1 · answered by GusBsAs 6 · 1⤊ 0⤋

1-cos^2x = sin^2x
1+cot^2x = csc^2x=1/sin^2x
so LHS = RHS = 1

2007-11-21 09:46:55 · answer #2 · answered by norman 7 · 1⤊ 0⤋

(1 - cos^2(x))(1 + cot^2(x))

=>sin^2(x) * [1 + (cos^2(x)/sin^2(x)]

=>sin^2(x)* [(sin^2(x)+ cos^2(x))/sin^2(x)]

=> sin^2(x) + cos^2(x) = 1

2007-11-21 09:59:54 · answer #3 · answered by mohanrao d 7 · 1⤊ 0⤋