Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)

1023 views

Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)

When proving trigonometric identites, we must show that the left hand side of the equation = the right hand side. Here we will start with the left hand side (LHS) and show that it is equivalent to the right hand side (RHS).

LHS=2sin(2x)-3cos(2x)-3sin(x)+3

Using the double angle rules for sin(2x) and cos(2x);

LHS=2(2sin(x)cos(x))-3(cos²(x)-sin²(x))-3sin(x)+3

Notice that the RHS has sin(x) factorised out, meaning that every term in the LHS has a common factor of sin(x). Currently the LHS has a cos²x term, but we can change this to a sin²x term using the identity: cos²(x)=1-sin²(x)

LHS=2(2cos(x)sin(x))-3(1-sin²(x)-sin²(x))-3sin(x)+3

=4cos(x)sin(x)-3(1-2sin²(x))-3sin(x)+3

=4cos(x)sin(x)-3+6sin²(x)-3sin(x)+3

=4cos(x)sin(x)+6sin²(x)-3sin(x)

=sin(x)(4cos(x)+6sin(x)-3)

=RHS

We have shown that LHS=RHS, therefore the proof is complete.

Joe B. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathematic...

11 months ago

Answered by Joe, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

434 SUBJECT SPECIALISTS

Rhianna C. 13 Plus Maths tutor, GCSE Maths tutor, A Level Maths tuto...

View profile

£20 /hr

Rhianna C.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry+ 1 more

“I am currently studying Maths at University and absolutely love it! I can't wait to share my enthusiasm with you!”

5.0

2 reviews | 14 completed tutorials

Save profile

Ruth N. GCSE Economics tutor, A Level Economics tutor, IB Economics t...

View profile

£22 /hr

Ruth N.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

5.0

11 reviews | 17 completed tutorials

Save profile

£26 /hr

George B.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

“Premium tutor. First class graduate with teaching experience from a top Russell Group university. I deliver fun and relaxed lessons which achieve results!”

5.0

95 reviews | 168 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

£36 /hr

Joe B.

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered:Maths, Further Mathematics + 3 more

“Hi! I'm Joe, a friendly, experienced and patient tutor with in-depth knowledge of both the old and new A Level Maths & Further Maths specifications.”

5.0

296 reviews | 299 completed tutorials

Save profile

Version:	3.49.9
Build:	5f485a18d000
Time:	2017-09-20T16:11:15Z

MYTUTOR SUBJECT ANSWERS

Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)

Still stuck? Get one-to-one help from a personally interviewed subject specialist

434 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Joe

Other A Level Maths questions

One-to-one help is at your fingertips