# Solving trigonomety equations using addition formulae.

• April 18th 2012, 07:16 PM
ImanAA
Solving trigonomety equations using addition formulae.
Can someone please explain to me, step by step how to arrive at the final answer. Im finding questions containing the theta sign rather than actual values for theta confusing.

I also dont know how to draw the theta sign on here so Ive just used x for ease.

The question is - Express the following as a single sine, cosine or tangent:

cos4x cos3x - sin4x sin3x

The solution I have breaks the answer down to cos(4x + 3x) which results in cos7x but I dont understand why this is also not the case for sine4x sin3x
• April 18th 2012, 07:17 PM
Prove It
Re: Solving trigonomety equations using addition formulae.
Quote:

Originally Posted by ImanAA
Can someone please explain to me, step by step how to arrive at the final answer. Im finding questions containing the theta sign rather than actual values for theta confusing.

I also dont know how to draw the theta sign on here so Ive just used x for ease.

The question is - Express the following as a single sine, cosine or tangent:

cos4x cos3x - sin4x sin3x

The solution I have breaks the answer down to cos(4x + 3x) which results in cos7x but I dont understand why this is also not the case for sine4x sin3x

Hint: \displaystyle \begin{align*} \cos{\left(\alpha + \beta\right)} &\equiv \cos{(\alpha)}\cos{(\beta)} - \sin{(\alpha)}\sin{(\beta)} \end{align*}
• April 18th 2012, 07:21 PM
ImanAA
Re: Solving trigonomety equations using addition formulae.
Im sorry, Im aware of that law but im still unable to use it and arrive at the answer for some reason.
• April 18th 2012, 07:51 PM
Prove It
Re: Solving trigonomety equations using addition formulae.
Quote:

Originally Posted by ImanAA
Im sorry, Im aware of that law but im still unable to use it and arrive at the answer for some reason.

What you have is exactly the same as the RHS of the identity I gave you...
• April 19th 2012, 02:38 AM
ImanAA
Re: Solving trigonomety equations using addition formulae.
That may be true but I need to know the full working out step by step otherwise I wouldn't get many marks in an exam. I know the final answer but I'm not looking for that.
• April 19th 2012, 02:49 AM
biffboy
Re: Solving trigonomety equations using addition formulae.
It's the whole expression that 'breaks down' to cos(4x+3x), not just the first part of it. You would get full marks for writing that the expression= cos(4x+3x) which = cos7x