# Homework Help: Simplification (Trigo Based)

1. Sep 4, 2008

### ritwik06

1. The problem statement, all variables and given/known data
Prove that:

$$sin^{2}(\theta+\alpha)+sin^{2}(\theta+\beta)-2sin(\theta+\alpha).sin(\theta+\beta).cos(\alpha-\beta)=sin^{2}(\alpha-\beta)$$

3. The attempt at a solution
After simplifying the LSH
by simply applying formula for sin(a+b) or cos(a+b) does give me this result but th method is too lengthy. Is there any other way out???????

2. Sep 4, 2008

### HallsofIvy

But since you have already done it one way, doing it any other way would just add to the work you have already done! Why would you want another way?

3. Sep 5, 2008

### ritwik06

Well, I shall be highly obliged if u could help me with a shorter method which requires lesser labor. I wish to learn new techniques to solve problems to save on time when such questions are asked in my exams :)

4. Sep 6, 2008

### ritwik06

Anybody interested to help me???

5. Sep 6, 2008

### tiny-tim

ping!

Hi ritwik06!
Yeah … why not!

Hint: this equation looks like the cosine rule for a triangle …

hmm …

ping! … draw the triangle, then apply the sine rule to it.