Find the angle x if sin2x + 2sinx - cosx - 1 = 0.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

sin2x + 2sinx - cosx - 1 = 0

We know that:

sin2x = 2sinx*cosx

Let us substitute:

==> 2sinx*cosx + 2sinx - cosx - 1 = 0

Now factor 2sinx:

==> 2sinx( cosx +1 ) - (cosx + 1) = 0

Now factor (cosx + 1):

==> (cosx+1) *(...

Get
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

sin2x + 2sinx - cosx - 1 = 0

We know that:

sin2x = 2sinx*cosx

Let us substitute:

==> 2sinx*cosx + 2sinx - cosx - 1 = 0

Now factor 2sinx:

==> 2sinx( cosx +1 ) - (cosx + 1) = 0

Now factor (cosx + 1):

==> (cosx+1) *( 2sinx - 1 ) = 0

Then we have two options:

cosx + 1 = 0       OR    2sinx - 1 = 0

==> cosx = -1       OR     sinx = 1/2

==> x1= pi + 2kpi

==> x2= pi/6 + 2kpi

==> x3= 5pi/6 + 2kpi

Then the answer is:

x= { pi+ 2kpi , pi/6 + 2kpi , 5pi/6 + 2kpi}

Approved by eNotes Editorial Team