Question

How do you rewrite `cos19cos5-sin19sin5` as a function of a single angle and then evaluate?

Answer 1

`cos19^@cos5^@-sin19^@sin5^@=0.9135`

Explanation:

Remember the formula for cosine for sum of angles,

`cos(A+B)=cosAcosB-sinAsinB`

As `cos19^@cos5^@-sin19^@sin5^@` is similar to the RHS above

`cos19^@cos5^@-sin19^@sin5^@=cos(19^@+5^@)=cos24^@`

and from tables / scientific calculators `cos24^@=0.9135`