Determine whether each of the following is an identity.
1. sin2θ - cos2θ = sinθ - cosθ
2. sin4θ - cos4θ = sin2θ - cos2θ
Show all necessary steps.
Trigonometric identities
2009-03-26 1:28 am
回答 (1)
2009-03-26 1:45 am
✔ 最佳答案
1. sin2θ - cos2θ = sinθ - cosθLHS
= sin2θ - cos2θ
= (sinθ + cosθ)(sinθ - cosθ)
so it is not an identity
2. sin4θ - cos4θ = sin2θ - cos2θ
LHS
= sin4θ - cos4θ
= (sin2θ + cos2θ)(sin2θ - cos2θ)
= (sin2θ - cos2θ)
= RHS
so it is an identity
收錄日期: 2021-04-23 18:23:12
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