What is x if (1+cos2x)/2=sin(-2x)?

Expert Answers

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

We have to solve (1 + cos 2x) / 2 = sin (-2x)

(1 + cos 2x) / 2 = sin (-2x)

=> -(1 + cos 2x) / 2 = sin (2x)

=> -( 1 + (cos x)^2 - (sin x)^2)/ 2 = 2 sin x cos x

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

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

=> - 2(cos x)^2  = 4 sin x cos x

=> -2 cos x = 4 sin x

=> sin x / cos x = -2/4

=> tan x = -1/2

x = arc tan (-1/2)

Therefore x = arc tan ( -1/2) + n*pi

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial