Question

cos45 cos30 + sin45 sin30

Answer 1

We know that:

Cos(A).cos(B) + sin(A).sin(B) = cos(A-B)

Similarly,

cos(45).cos(30) + sin(45).sin(30)

= cos(45-30)

= cos(15°)

= $\frac{√3 + 1}{2√2}$

Answer 2

Answer:

$\cos(45) \cos(30 ) + \sin(45) + \sin(30 ) \\ = \cos(45 - 30) \\ = \cos(15)$

or,

$\cos(45) \cos(30) + \sin(45) \sin(30) \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ = \frac{ \sqrt{3} + 1 }{2 \sqrt{2} }$

Step-by-step explanation:

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