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
