SOLUTION: A*sin(X)+B*sin(X+U)=C*sin(X+W), with C=sqrt(A^2+B^2+2*A*B*cos(U)) and tan(W)=(B*sin(U))/(A+B*cos(U)). What are the intermediate steps leading to this result?

Algebra.Com
Question 1087083: A*sin(X)+B*sin(X+U)=C*sin(X+W), with C=sqrt(A^2+B^2+2*A*B*cos(U))
and tan(W)=(B*sin(U))/(A+B*cos(U)).
What are the intermediate steps leading to this result?
Answer by Edwin McCravy(20086)   (Show Source): You can put this solution on YOUR website!
A*sin(X)+B*sin(X+U)=C*sin(X+W), with C=sqrt(A^2+B^2+2*A*B*cos(U))
and tan(W)=(B*sin(U))/(A+B*cos(U)).
We are given that  tan(W)=(B*sin(U))/(A+B*cos(U)).

Since  and

,

we can draw a right triangle with B*sin(U) as the
opposite side of angle W and A+B*cos(U) as the
adjacent side of W:

 

We calculate the hypotenuse:















Notice that this result is the exact value that was given for C. So





Let's start with right side of what we have to prove:




Since  and ,
we use the right triangle above to substitute for cos(W) and sin(W)













Edwin
RELATED QUESTIONS

Find the exact value of the trigonometric function given that sin u = -12/13 and cos v =... (answered by MathLover1,MathTherapy)
How would you verify the identify of sec y cos {{{ y = 1 }}}? A.) 1 + tan˛u = sec˛ u... (answered by josgarithmetic)
Derive the half angle formula for sin( u/2 ) by following the steps below. (a) Use the... (answered by richard1234)
Factor completely: sin^3(x) + cos^3(x) Select one: a. (sin(x) + cos(x))(sin^2(x) -... (answered by Alan3354)
Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5 where... (answered by Fombitz)
Need help!!!! Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u=... (answered by lwsshak3)
How would you verify the identify of sec y cos {{{ y = 1 }}}?... (answered by Fombitz)