If 180°< α< 270°, cos⁡ α=−8/17, 270°< β< 360°, and sin⁡ β=−4/5, what is cos⁡(α+β)?

cos(\alpha+\beta)=-\frac{84}{85}

Step-by-step explanation:

we know that

Remember the identity

step 1

Find the value of  

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

Find the value of sine

substitute

step 2

Find the value of  

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

Find the value of cosine

substitute

step 3

Find cos⁡ (α + β)

we have

substitute

351.23

step-by-step explanation: