It is known that θ is a positive acute angle, and sin θ + cos θ is proved Sin θ + cos θ = sin (θ + 45 °) twice the root sign

Sin θ + cos θ = √ 2 (sin θ * √ 2 / 2 + cos θ * √ 2 / 2) because sin (α + β) = sin α cos β + cos α sin β, and sin45 = cos45 = √ 2 / 2, so sin θ * √ 2 / 2 + cos θ * √ 2 / 2 = sin θ * cos45 + cos θ * sin45 = sin (θ + 45 °), so sin θ + cos θ = √ 2 (sin θ * √ 2 / 2 + cos

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