Question

prove that sina+cosa/sina-cosa+sina-cosa/sina+cosa=2/2sin^a-1

Answer 1

I think you mean

(sina+cosa)/(sina-cosa)+(sina-cosa)/(sina+cosa)=2/2sin²a-1

Let us do the proof

First take LCM :

[(sina+cosa)² - (sina-cosa)²] / (sin²a-cos²a)

⇒2(sin²a+cos²a)/ (sin²a - (1-sin²a))

⇒2(1)/(2sin²a-1)

⇒2/(2sin²a-1)

proof completed.

(I am an eight standard student who qualified for RMO this year. I am basically a maths genius... I am not bragging, its a fact. So, if you have any mathematics related doubt feel free to ask me)