Question

Cos(a+b)+2sina×sinbпомогите решить

Answer 1

Cos(α+β) = cos(α)·cos(β) - sin(α)·sin(β)
cos(α)·cos(β) - sin(α)·sin(β)+2sina*sinb=cos(α)·cos(β) + sin(α)·sin(β)=
=cos(α-β)

Answer 2

To solve this expression, we can use the trigonometric identity:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

So, substituting this identity into the expression we have:

cos(a+b) + 2sin(a)sin(b) = cos(a)cos(b) - sin(a)sin(b) + 2sin(a)sin(b)

Simplifying, we get:

cos(a+b) + 2sin(a)sin(b) = cos(a)cos(b) + sin(a)sin(b)

Now, we can use another trigonometric identity:

sin(a)sin(b) + cos(a)cos(b) = cos(a-b)

Substituting this identity, we get:

cos(a+b) + 2sin(a)sin(b) = cos(a-b)

Therefore, we have:

cos(a+b) = cos(a-b) - 2sin(a)sin(b)

This is the final expression for cos(a+b) + 2sin(a)sin(b).