Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

790,612 users

How do you show that

0 votes

2sinx(cosx+cos3x)=sin4x?

asked Apr 15, 2013 in TRIGONOMETRY by andrew Scholar

1 Answer

0 votes

2sinx(cos3x + cosx)

Recall : Trigonometry formulas cos3x = 4cos3x - 3cosx

Substitute cos3x = 4cos3x - 3cosx

2sinx(4cos3x - 3cosx + cosx)

2sinx(4cos3x - 2cosx)

2sinx(2cosx(2cos2x - 1))

Recall : trigonometry formulas sin2x = 2sinxcosx

2sin2x(2cos2x - 1)

Recall : cos2x = cos2x - sin2x = 2cos2x - 1

Substitute 2cos2x - 1 = cos2x

2sin2xcos2x

Sustitute 2sin2xcos2x = sin4x

sin4x.

answered Apr 15, 2013 by diane Scholar

Related questions

asked Jul 19, 2014 in TRIGONOMETRY by anonymous
asked Apr 9, 2016 in PRECALCULUS by anonymous
...