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).


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


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) 







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

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

5 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


£36 /hr

Andres O.

Degree: PhD in Theoretical Particle Physics (Doctorate) - Durham University

Subjects offered:Maths, Physics+ 2 more

-Oxbridge Preparation-

“I am a patient and experienced tutor with a lot of enthusiasm for Mathematics and Physics. ”

George S. GCSE Further Mathematics  tutor, A Level Further Mathematic...
£20 /hr

George S.

Degree: Physics (Masters) - Birmingham University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics

“About Me: I am just entering my first year to study Physics at University of Birmingham, I've always enjoyed anything maths based hence my A-level choices, I hope I can help you through your work whether it's GCSE or A-level and maybe...”

£20 /hr

Aimee F.

Degree: Economics (Bachelors) - Leeds University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics
-Personal Statements-

“Hi, I'm Aimee and I study Economics at the University of Leeds. I am happy to help students in Economics and Math as they are two subjects I really love. I am patient and understanding and will happily go through things as many times ...”

About the author

Joe B.

Currently unavailable: for new students

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered:Maths, Further Mathematics + 4 more

Further Mathematics
-Personal Statements-

“About Me Hi, I'm Joe, a first year mathematics student from Luton studying at Bath University. I am an accomplished mathematician and economist, having achieved A* grades in A Level Maths, Further Maths and Economics in June 2016. As ...”

You may also like...

Posts by Joe

Find arsinh(x) in terms of x

Find the nth term of the sequence 7,11,15,19...

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

Other A Level Maths questions

y=sin(x)cos(x). Find dy/dx

How can I remember the difference between differentiation and integration?

Mechanics 1: How do you calculate the magnitude of impulse exerted on a particle during a collision of two particles, given their masses and velocities.

How do you differentiate X to the power of a?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss