- #1

unique_pavadrin

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## Homework Statement

Given that f(x)=sin(2x), find x such that f(2x+1)=1

## Homework Equations

f(2x+1)=1

f(2x+1)=sin(4x+2)

sin(4x+2)=1

## The Attempt at a Solution

sin(4x+2)=1

sin(4x+2)=sin(4x)cos(2)+cos(4x)sin(2)

sin(4x+2)=(2sin(2x)cos(2x))cos2+cos^2(2x)sin^2(2x)sin2

sin(4x+2)=(2(2sin(x)cos(x))(2cos^2(x)-1)cos(2)+cos^2(2x)sin^2(2x)sin(2)

sin(4x+2)=4sin(x)2cos^4(x)-cos(2)+2cos^2(x).....

That is how I am trying to solve to this equation, by using the compound angle formula and the double angle formula, however it seems as i am going around in circles. The correct answer for this problem is equal to:

(pi-4)/8 +

*n*pi/2

Is there a simpler way of solving this equations and ones which are simpler, or am trying to solve it using the correct method. All help is greatly appreciated and many thanks in advance,

pavadrin