Verifying Sin2A = 2SinACosA with A=30deg

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To verify the identity Sin2A = 2SinACosA for A=30 degrees, first note that 2A means multiplying 30 degrees by two, resulting in 60 degrees. The verification involves calculating both sides: the left side requires finding sin(60 degrees), while the right side involves calculating 2*sin(30 degrees)*cos(30 degrees). Using known values from the 30°-60°-90° triangle, sin(60°) equals √3/2, sin(30°) equals 1/2, and cos(30°) equals √3/2. By substituting these values, both sides of the equation can be shown to be equal, confirming the identity. This approach emphasizes direct calculation rather than manipulation of trigonometric identities.
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Homework Statement


If A= 30 deg.. verify that..
Sin2A = 2SinACosA
First off..On the left side where it says 2A... does that mean multiply 30deg by two? and on the right side does the two also mean multiply?

Anyways... since it is asking me to verify that they are equal... am i basically using the trig identities to prove that this statement is true by only working with one side and trying to make is look like the other side.?


Homework Equations





The Attempt at a Solution

 
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Since this is a trig identity that is always true, I don't think they want you to use trig identities to show it. I think they just want you to calculate
sin(60 degrees) on the left hand side and 2*sin(30degrees)*cos(30degrees) on the right hand side and verify that they are equal.
 
Alright... So I was correct when they said multiply two by the deg on the left side? This is all new to me... So how would you calculate that they are equivalent?
 
It's quite simple. Evaluate sin 60°, sin 30°, and cos° 30 (using the knowledge of the 30°-60°-90° triangle) and plug into sin 60° = 2 sin 30° cos 30° to verify.
 

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