Question #7a284

1 Answer
A08
Apr 14, 2017

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

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