Question

sin 3θ= cos(θ-26) Solve for θ

Answer 1

[tex]Sin 3 \alpha = cos ( \alpha - 26) \\ sin 3 \alpha = Sin (90 + \alpha - 26) \\ 3 \alpha = 64 + \alpha \ \ or \ \ 3 \alpha = 180 - (64 + \alpha ) \\ So, 2 \alpha = 64\ \ or 4 \alpha = 116 \\ \alpha = 32\ deg\ \ OR\ \ alpha = 29\ deg \\ [/tex]

Here we use sin 90+α = cos α

Answer 2

Given :

• sin3θ = cos(θ - 26°)

To Find :

• Value of θ

Solution :

⟹ sin3θ = cos(θ - 26°)

⟹ sin3θ = sin [90° - (θ - 26°) ]

⟹ sin3θ = sin [90° - θ + 26°]

⟹ 3θ = 90° - θ + 26°

⟹ 3θ + θ = 90° + 26°

⟹ 4θ = 90° + 26°

⟹ 4θ = 116°

⟹ θ = 116° / 4

⟹ θ = 29°

Thus Value of θ = 29°

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