Question

Simplify cos5cos40-sin5cos40

Answer 1

= sin(40+50)
= sin 90
= 1

Answer 2

Answer:

cos(5)cos(40) - sin(5)cos(40) = cos(45) = √(2)/2

Step-by-step explanation:

One of the trig identity (Angle Sum/Difference Identity) is:

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

We're given: cos(5)cos(40) - sin(5)cos(40)

In this case, α=5 and β=40

Plug it into you're equation

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

cos(5 + 40) = cos(5)cos(40) - sin(5)cos(40)

cos(5 + 40) = cos(45) = √(2)/2