Question

I really need help oof-

Angle α lies in quadrant II, and tanα=−12/5 . Angle β lies in quadrant IV, and cosβ=3/5.

What is the exact value of cos(α−β) ?

Enter your answer in the box.

cos(α−β) = __

Answer 1

From the given info (and the linked question) we find

`\cos\alpha=-\frac5{13}`

`\sin\alpha=(12)/(13)`

`\sin\beta=-\frac45`

Then using the angle-sum identity for cosine, we have

`\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta`

`\cos(\alpha-\beta)=\left(-\frac5{13}\right)\frac35+(12)/(13)\left(-\frac45\right)=-(63)/(65)`