Question

Cos 5π/8*Cos 3π/8+Sin 5π/8*Sin 3π/8

Answer 1

cos(5П/8)*cos(3П/8)+sin(5П/8)*sin(3П/8)=cos(5π/8-3π/8)=cos(2π/8)=cos(π/4)=1/√2

Answer 2

The expression you've provided is a special case of the trigonometric identity known as the angle sum formula for cosine:

cos(α) * cos(β) + sin(α) * sin(β) = cos(α - β),

where α and β are angles.

In your expression:

• α = 5π/8
• β = 3π/8

So, using the angle sum formula:

cos(5π/8) * cos(3π/8) + sin(5π/8) * sin(3π/8) = cos(5π/8 - 3π/8)

Simplifying the subtraction of the angles:

cos(5π/8 - 3π/8) = cos(π/4)

Now, the cosine of π/4 is equal to √2/2:

cos(π/4) = √2/2

Therefore, the value of the expression is √2/2.