Find the value of the given expression \(\frac{{cos\theta \; + \;sin\

1.	Find the value of the given expression \(\frac{{cos\theta \; + \;sin\theta }}{{\sqrt {1\; + \;sin2\theta } }}\)1. sinθ + cosθ 2. 03. 14. sinθ - cosθ
Answer» Correct Answer - Option 3 : 1 Given: Our given expression is \(\frac{{cos\theta \; + \;sin\theta }}{{\sqrt {1\; + \;sin2\theta } }}\) Formula used: sin2θ = 2sinθ cosθ sin²θ + cos²θ = 1 (a + b)² = a² + b² + 2ab Calculation: Our given expression is \(\frac{{cos\theta \; + \;sin\theta }}{{\sqrt {1\; + \;sin2\theta } }}\) ⇒ (cosθ + sinθ)/√(sin²θ + cos²θ + 2sinθ cosθ) ⇒ (cosθ + sinθ)/√(sinθ + cosθ)² ⇒ (cosθ + sinθ)/(sinθ + cosθ) ⇒ 1 ∴ The value of the given expression is 1

Find the value of the given expression \(\frac{{cos\theta \; + \;sin\theta }}{{\sqrt {1\; + \;sin2\theta } }}\)1. sinθ + cosθ 2. 03. 14. sinθ - cosθ

Answer» Correct Answer - Option 3 : 1

Given:

Our given expression is \(\frac{{cos\theta \; + \;sin\theta }}{{\sqrt {1\; + \;sin2\theta } }}\)

Formula used:

sin2θ = 2sinθ cosθ

sin²θ + cos²θ = 1

(a + b)² = a² + b² + 2ab

Calculation:

Our given expression is \(\frac{{cos\theta \; + \;sin\theta }}{{\sqrt {1\; + \;sin2\theta } }}\)

⇒ (cosθ + sinθ)/√(sin²θ + cos²θ + 2sinθ cosθ)

⇒ (cosθ + sinθ)/√(sinθ + cosθ)²

⇒ (cosθ + sinθ)/(sinθ + cosθ)

⇒ 1

∴ The value of the given expression is 1