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    The value of cos 75o75^o75o + sin 15o15^o15o is equal to:​
    Question

    The value of cos 75o75^o + sin 15o15^o is equal to:​

    A.

    312\frac{\sqrt{3} - 1}{\sqrt{2}}​​

    B.

    32\frac{\sqrt{3}}{\sqrt{2}}​​

    C.

    23\frac{\sqrt{2}}{\sqrt{3}}​​

    D.

    3+12\frac{\sqrt{3} + 1}{\sqrt{2}}​​

    Correct option is A

    Given: 

    cos75°+sin15°\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°)

    =>2×(12×3212×12)=>2×3122=>312\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}​​​

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