SOLUTION: He all, I have some difficulties understanding the reason about the solution of this equation: sin(x+π/3) = cos2x proposed in the book, namely: x= π/18+2kπ/3

Algebra ->  Trigonometry-basics -> SOLUTION: He all, I have some difficulties understanding the reason about the solution of this equation: sin(x+π/3) = cos2x proposed in the book, namely: x= π/18+2kπ/3       Log On


   

Question 1033152: He all,
I have some difficulties understanding the reason about the solution of this equation:
sin(x+π/3) = cos2x
proposed in the book, namely:
x= π/18+2kπ/3 V x= -π/6+2kπ

My solution after converting to sin(x+π/3) = sin(π/2-2x) is:
x= π/18+kπ/9 V x= -π/6-kπ/3
Can somebody explain me step by step how to come to the
solution of the book?
Thank you very much in advance
RB

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sin(x+π/3) = cos2x
proposed in the book, namely:
x= π/18+2kπ/3 V x= -π/6+2kπ
-------
since sin(K) = cos((pi/2)-K) you can make a change on the left side::
cos((pi/2)-(x+(pi/3))) = cos(2x)
-----------
(pi/2)-x-(pi/3) = 2x
3x = [(3pi-2pi)/6]
----
x = pi/18 + 2kpi ; x = -pi/18 + 2kpi
----------------------------------------
Cheers,
Stan H.