Question

Anyone help please!!!!

Answer 1

cos(a-B)-cos(a+B)
cosucosv - sinusinv = cos(u+v)
cosucosv + sinusinv = cos(u-v)

cos(a-B)-cos(a+ B) = cosa cosB + sina sinB - (cosa cosB - sina sinB)= cosa cosB + sina sinB - cosacosB + sinb sinB= 2 sina sinB

Answer 2

We are to verify the identity:

cos(α-B)-cos(α+B) = 2 sinα sinβ

Left hand side = cos(α - B)-cos(α + B) 

= cosα cosβ + sinα sinB - (cosα cosB - sinα sinβ)

= cosα cosβ + sinα sinB - cosα cosB + sinα sinβ)

= sinα sinβ + sinα sinβ

= 2 sinα sinβ

= Right Hand side