Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How would I solve the following question?

Show that

$$2\sin(127.5)\sin(97.5)=(\sqrt{3}+\sqrt{2})/2$$

My work is I know

$$\sin A\sin B=(-1/2)(\cos(A+B)-\cos(A-B))$$

So I did

$$(-1/2)(\cos(127.5+97.5)-\cos(127.5-97.5))$$

but I do not get the correct answer.

share|improve this question
1  
What do you get? –  M Turgeon Aug 3 '12 at 19:20
add comment

2 Answers 2

I assume that 127.5 and 97.5 are given in degrees, not radians, and will write $127.5^\circ$ and $97.5^\circ$ instead.

The step $-\frac{1}{2} (\cos (127.5^\circ + 97.5^\circ) - \cos(127.5^\circ - 97.5^\circ))$ is correct. Now, note that $127.5 + 97.5 = 225 = 180 + 45$ and $127.5 - 97.5 = 30$. Since $\cos 180^\circ + \alpha = -\cos \alpha$, this reduces to $-\frac{1}{2} (-\cos 45^\circ -\cos 30^\circ)$. Can you do the rest yourself?

share|improve this answer
    
@EdGorcenski Well, my computations give the right result. Maybe you forgot the factor of 2 in front of the signs...? –  M Turgeon Aug 3 '12 at 19:18
1  
@MTurgeon I had some mis-placed parenthesis! I just re-ran the computation to verify it is indeed correct. –  Arkamis Aug 3 '12 at 19:20
add comment

The equation you have for $\sin A \cdot \sin B$ is incorrect (sign flip). It should be: $$ \sin A \cdot \sin B = \frac{1}{2}\cos(A-B) - \frac{1}{2}\cos(A+B) $$ or $$ \sin A \cdot \sin B = -\frac{1}{2}\cos(A+B) + \frac{1}{2}\cos(A-B) $$ $+, -, -, +$ OR $-, +, +, -$

share|improve this answer
add comment

Your Answer

 
discard

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.