Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30°

Q) Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30°

Ans: Here, let’s start values of sin & cosine for θ = 30⁰ and 45⁰

We know that sin 30⁰= $\frac{1}{2}$ , cos 30⁰ = $\frac{\sqrt 3}{2}$ , cos 45⁰ = $\frac{1}{\sqrt 2}$

We submit these values in the given question, we get:

2√2 cos 45° sin 30° + 2√3 cos 30°

= 2√2 $(\frac{1}{\sqrt 2}) (\frac{1}{2})$ + 2√3 $(\frac{\sqrt 3}{2})$

= $\frac {2 \sqrt 2}{2 \sqrt 2} + \frac {2 \sqrt 3 \times \sqrt 3}{2}$

= 1 + 3 = 4

Therefore, the value of 2√2 cos 45° sin 30° + 2√3 cos 30° = 4.

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