consider the derivation of sin(2x). where is the error? step 1. sin(2x)=sin(x + x) 2. =sin(x)cos(x)+cos(x)sin…

consider the derivation of sin(2x). where is the error? step 1. sin(2x)=sin(x + x) 2. =sin(x)cos(x)+cos(x)sin(x) 3. =(sin(x)cos(x))² o step 2 should read = cos(x)cos(x) - sin(x)sin(x). o step 2 should read = sin(x)cos(x) - cos(x)sin(x). o step 3 should read = - 2sin(x)cos(x). o step 3 should read = 2sin(x)cos(x).

consider the derivation of sin(2x). where is the error? step 1. sin(2x)=sin(x + x) 2. =sin(x)cos(x)+cos(x)sin(x) 3. =(sin(x)cos(x))² o step 2 should read = cos(x)cos(x) - sin(x)sin(x). o step 2 should read = sin(x)cos(x) - cos(x)sin(x). o step 3 should read = - 2sin(x)cos(x). o step 3 should read = 2sin(x)cos(x).

Answer

Explanation:

Step1: Recall sum - formula for sine

The formula for $\sin(A + B)=\sin(A)\cos(B)+\cos(A)\sin(B)$. When $A = B=x$, we have $\sin(x + x)=\sin(x)\cos(x)+\cos(x)\sin(x)$, so step 1 and 2 are correct.

Step2: Simplify step 2

$\sin(x)\cos(x)+\cos(x)\sin(x)=2\sin(x)\cos(x)$. The error is in step 3 where the addition was wrongly turned into multiplication.

Answer:

Step 3 should read = 2sin(x)cos(x).