Simplifying Trigo Equations: Is There a Shortcut?

[ritwik06]

Homework Statement

Prove that:

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

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??

 

[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?

 

[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 :)

 

[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 :)

Anybody interested to help me?

 

[tiny-tim]

ping!

Hi ritwik06!

I wish to learn new techniques to solve problems to save on time when such questions are asked in my exams :)

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.