SOLUTION: Find the general solution √3cosx+sinx=1

Algebra.Com
Question 1058139: Find the general solution √3cosx+sinx=1
Answer by ikleyn(52809)   (Show Source): You can put this solution on YOUR website!
.
Find the general solution √3cosx+sinx=1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 = .

Multiply both sides by . You will get

 = .           (1)

Notice that  = ,  = . 

Substitute it into the left side of (1). You will get

 = .    (2)

Apply the formula sin(a)*cos(b) + cos(a)*sin(b) = sin(a+b) to the left side of (2). You ill get

 = .                       (3)

It implies 

 = ,  k = 0, +/-1, +/-2, . . . or

 = ,  k = 0, +/-1, +/-2, . . .


Thus there are two sets of solutions:

1.  x =  = ,  which is equivalent to  x = ,


and the other family


2.  x =  = 


Answer.  There are two sets of solutions:  1)  x =   and  2)  x = ,  k = 0, +/-1, +/-2, . . .

The plot below confirms these solutions.



Plots y = and y = 1


RELATED QUESTIONS

Find the general solution of... (answered by greenestamps)
1-sinx = square root 3cosx On the interval (0, 360) Find all solutions (answered by jsmallt9)
Solve the general solution of y'''+ 4y'= x+3cosx by undertermine coeeficient. Find... (answered by Edwin McCravy)
find the general solution of the following equation... (answered by lwsshak3)
find the general solution for the equation 2sin^2x-sinx=1. Answer in... (answered by stanbon)
Please Find the general solution of: sin3x-sinx=... (answered by ikleyn)
Find the general solution to... (answered by ikleyn)
Find a rectangular form of the equation r(sinx + 3cosx) = 4. Thank you for your... (answered by KMST)
using cos3x= 4cos^3x -3cosx find the general solution for cos3x+2cosx=0 Soln:... (answered by lwsshak3,deepakpradhan)