Question

Question #7a284

Answer 1

I get
`cosx`

Explanation:

We know the Sum Formulae
`sin(A+B)=sinAcosB+cosAsinB`
and
`cos(A+B)=cosAcosB-sinAsinB`

The given expression becomes
`sin (x+30^@)+cos (x+60^@)`
`=>sinxcos30^@+cosxsin30^@+cosxcos60^@-sinxsin60^@`

We also know that
`cos30^@=sqrt3/2`, `sin30^@=1/2`, `cos60^@=1/2`, `sin60^@=sqrt3/2`
Inserting these values we get
`(sinx)sqrt3/2+(cosx)1/2+(cosx)1/2-(sinx)sqrt3/2`
`=>cosx`