1
$\begingroup$

How does $\sin \theta \times \sin (\theta - \phi)$ become $\frac{\cos \phi - \cos (2\theta-\phi)}{2}$

$\endgroup$
  • 1
    $\begingroup$ I recommend using something other than $\varnothing$ for an angle, or number. It by convention (that I have never seen broken) is the empty set. $\endgroup$ – Paul Plummer Mar 24 '15 at 7:28
  • $\begingroup$ @PaulPlummer - the OP probably wanted to write $\phi$ here. $\endgroup$ – 299792458 Mar 24 '15 at 7:29
  • 1
    $\begingroup$ @TheDarkSide I could tell (and was about to submit an edit before someone got to it before I did), just letting the author know for any future posts. $\endgroup$ – Paul Plummer Mar 24 '15 at 7:31
  • $\begingroup$ @PaulPlummer Yeah.will do.Thanks $\endgroup$ – techno Mar 24 '15 at 9:19
2
$\begingroup$

Directly expanding the LHS would be a difficult way of going about it, since there would have to be so many simplifications. Instead, proceed as follows:

Use the identities

$$ \cos (A \pm B) = \cos A \cos B \mp \sin A \sin B$$

to arrive at

$$ \sin A \sin B = \left(\cos (A-B) - \cos (A+B) \right)/2$$

Then, your answer follows in one step. Note that cosine function is even under parity, so that $\cos(-\theta) = \cos(\theta)$.

$\endgroup$
1
$\begingroup$

SUBSTITUTE FORMULE FOR SIN(A-B) AND (SIN^2θ) AND LASTLY GET THE EQUATION IN FORM OF COS(A-B) :)

$\endgroup$
  • 2
    $\begingroup$ Don't use all caps. Also, it is frowned upon to post a photo in most instances (and I think this is one of those). You may want to learn some MathJax so that you can provide answer that are easier to read and better formated. A tutorial can be found here $\endgroup$ – Paul Plummer Mar 24 '15 at 7:45
  • $\begingroup$ Thx!!a lot!! the link was very helpful... @PaulPlummer $\endgroup$ – Suhaas Mar 24 '15 at 9:08
  • 1
    $\begingroup$ Thanks for writing this,i have upvoted it.But i will select the first answer as its simple. $\endgroup$ – techno Mar 24 '15 at 15:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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