Find the general solution of 3 sin 4 θ + cos 4 θ = 1

Find the general solution of 3sin4θ+cos4θ=1
  1. nπ only
  2. nπ+π4 only
  3. nπ-π4 only
  4. nπ, nπ+π4 and nπ-π4

Solution

3sin4θ+cos4θ=1

⇒3sin4θ=(1-cos2θ)(1+cos2θ)

⇒3sin4θ=sin2θ·2-sin2θ

sin2θ=0, 3sin2θ=2-sin2θ

⇒sin2θ=12

θ=nπ, n∈z

⇒θ=nπ±π4, m∈z

Asked in: AP EAMCET 2020 (23 Sep Shift 1)

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