The value of cos $$75^o$$ + sin $$15^o$$ is equal to:​

Correct option is A

Given: 

​$$\cos 75\degree + \sin 15\degree$$​​

Formula used:

Cos (90° - θ) = Sin θ 

Sin (α - β) = Sinα Cosβ - Sinβ Cosα

Solution:

cos 75° + sin 15°

=> Cos (90° - 15°) + sin 15°

=> sin 15° + sin 15°

=> 2 × sin 15°

=> 2 × Sin (45° - 30°)

=> 2 × (Sin 45° Cos 30° - Sin 30° Cos45°)

​$$\begin{aligned}& \Rightarrow 2 \times\left(\frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2}-\frac{1}{2} \times \frac{1}{\sqrt{2}}\right) \\& \Rightarrow 2 \times \frac{\sqrt{3}-1}{2 \sqrt{2}} \\& \Rightarrow \frac{\sqrt{3}-1}{\sqrt{2}}\end{aligned}$$​​​