Is sin 2x sin x - cos x = sqrt 3/4 true for x = 7pi/6?

Expert Answers

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

For the sine function : sin (x + 2pi) = sin x and sin (x + pi)= -sin x and for the cosine function , cos ( x + pi) = -cos x.

sin 2x sin x - cos x, for x = 7pi/6

=> sin 14pi/6 * sin 7pi/6 - cos 7pi/6

=> sin ( 2pi/6 + 2pi) * sin (pi/6 + pi) - cos( pi + pi/6)

=> - sin 2pi/6 * sin pi/6 + cos pi/6

Now sin 2pi/6 = .5 and cos pi/6 = sqrt 3/2

=> -(sqrt 3/ 2)(1/2) + sqrt 3/2

=> -sqrt 3 / 4 + 2*sqrt 3 / 4

=> sqrt 3 / 4

For x = 7pi/6, therefore sin 2x sin x - cos x = sqrt 3/ 4

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