Question

How do you find the exact value of the expression by using appropriate identities `sin(79)cos(49)-cos(79)sin(49)`?

Answer 1

Apply the angle addition formula to find that
`sin(79^@)cos(49^@)-cos(79^@)sin(49^@)= 1/2`

Explanation:

Using the identity
`sin(alpha - beta) = sin(alpha)cos(beta)-cos(alpha)sin(beta)`

`sin(79^@)cos(49^@)-cos(79^@)sin(49^@) = sin(79^@-49^@)`

`= sin(30^@)`

`= 1/2`