which expression completes the identity sin ucosv=?
Which expression completes the identity sin u + sin v = ?
To complete the identity sin ucos v, we can use the trigonometric identity of the product of sines and cosines, which is:
sin ucos v = 0.5 * (sin(u+v) + sin(u-v))
This equation provides the complete expression to evaluate sin ucos v.
To complete the identity sin(u)cos(v), we need to find an expression that can replace the question mark.
One way to find the answer is to use a trigonometric identity. In this case, we can use the sine of the sum formula, which states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
By substituting u for A and v for B, we have:
sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
From this, we can see that the expression sin(u + v) would complete the given identity sin(u)cos(v) = ?. Therefore, the answer is sin(u + v).
we have
sin(u+v) = sinu cosv + cosu sinv
sin(u-v) = sinu cosv - cosu sinv
add them up and you have
sin(u+v)+sin(u-v) = 2sinu cosv
now just finish it up.