Question

Help with trig

Answer 1

Verify the following identity: sin(a + β) + sin(a − β) = 2sinacosβ

Answer 2

S: Doesn't verifying meaning showing it shows every step?

Answer 3

use your addition and subtraction formula for sine.
Yes verify means you want to prove that the statement is true.
SO you would do:
LHS = sin(a + β) + sin(a − β)
And then you want to expand using the addition and subtraction formulas and then eventually you want to reach
= 2sinacosβ
And then you write = RHS
Therefore since you proved the LHS = RHS therefore you just verified the statement :)

Answer 4

so starting with the left side it works out into: sin(α)cos(β) + cos(α)sin(B)+ sin(α)cos(β) – cos(α)sin(β)? is this what you mean?

Answer 5

exactly! :)
Then you can simplify, collect like terms and cancel things out right? :P

Answer 6

cos(a)(-sin(b))+2sin(a)cos(b)+cos(a)+sin(b)

Answer 7

O_O how did you get that?
You worked out that the
LHS = sin(α)cos(β) + cos(α)sin(B)+ sin(α)cos(β) – cos(α)sin(β)

So now you can rearrange the equation if you'd like to make it simpler :)
LHS = sin(α)cos(β) + sin(α)cos(β) + cos(α)sin(B) – cos(α)sin(β)

Now can you see that " cos(α)sin(β)" and " – cos(α)sin(β)" will cancel out and then you will be left with "sin(α)cos(β) + sin(α)cos(β) "
So that equals to ?

Answer 8

2sin(a)cos(b)? Egh i suck at simplifying it seems

Answer 9

yeep! That's it.
Though it would be 2sin(α)cos(β) :)
Just think of it like "like terms" and you'll be fine

Answer 10

and what we just worked out equals to the right hand side right?
THEREFORE you just finished the question :)

Answer 11

Thank you so much