Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$\sin((n+1)x) \sin((n+2)x)+\cos((n+1)x) \cos((n+2)x)=\cos(x)$

Hi, I have been trying to solve this trigonometric function since last hour but not able to please help me to solve the above trigonometric function.

share|cite|improve this question
up vote 3 down vote accepted

We use the subtraction rule for cosines: $$\cos(a-b)=\cos a\cos b+\sin a\sin b.\tag{$1$}$$ Put $a=(n+2)x$ and $b=(n+1)x$. The right-hand side of $(1)$ is then the complicated expression you were given, except yours mentioned the sines first.

So your expression is equal to $\cos\left((n+2)x-(n+1)x\right)$. But $(n+2)x-(n+1)x=x$.

share|cite|improve this answer
Thank you for helping. – Drownpc Aug 29 '12 at 7:06

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.