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Please see formatting instructions below the problem.

Prove the identity
sin ( α + β ) + sin ( α − β )

2 sin ( α ) cos ( β )

We will work on the left side:	  

sin ( α + β ) + sin ( α − β )

=

1. Use sum and difference identities (type "alpha" for
   α and "beta" for
   β ):

=

Now you have:	

2 sin ( α ) cos ( β )

=

2. Simplify:

=

Proven! Now you have:	  
  	 

FORMATTING INSTRUCTIONS BELOW Type in lowercase and use parentheses. For example type sin(x) not sinx.

For fractions use the divide symbol "/". For example sin(x)/cos(x) for
sin ( x ) cos ( x )

For multiplication of fractions use parentheses. For example (cos(a)/sin(b))(tan(c)/sin(d)) for
( cos ( a ) sin ( b ) ) ( tan ( c ) sin ( d ) ) .

For multiplication without fractions no symbol is necessary. For example cos(a)sin(b)

For exponents use "^". Parentheses will be necessary depending on how you choose to type your answer For example sin^2(x) for
sin 2 ( x ) . Or (sin(x))^2 for
( sin ( x ) ) 2 . For fractions with multiple terms in the numerator or denominator parentheses are necessary. For example (1+sin(x))/cos(x) for
1 + sin ( x ) cos ( x ) . Or (1+sin(x))/(1-sin(x)) for
1 + sin ( x ) 1 − sin ( x )