Question

cos theta -sin theta =1 show that cos theta plus sin theta =1 or -1​

Answer 1

Answer:

explanation=>

$\bf \: correct \: question \mapsto \boxed{cos \theta+ sin \theta =1} \\ \bf\:prove \: that \: cos \theta - sin \theta =\pm\:1 \\ \\ \\\bf\huge{solution==>}$

$\bf \: Given \: that, cosθ + sinθ = 1 \\\bf ⇒ (cosθ + sinθ)² = 1²\\ \bf⇒ cos²θ + sin²θ + 2 sinθ cosθ = 1 \\\bf ⇒ 1 + 2 sinθ cosθ = 1 \\\bf ⇒ 2 sinθ cosθ = 0 \\ \bf⇒ sinθ cosθ = 0 \\ \bf \: Now, (cosθ - sinθ)² \\\bf \mapsto (cosθ + sinθ)² - 4 sinθ cosθ \\ \bf \mapsto 1² - (4 × 0) \\ \bf \mapsto 1 - 0 \\ \bf \mapsto 1 \\ \bf⇒ (cosθ - sinθ)² = 1 \\ \bf⇒ cosθ - sinθ = ± 1$