Question

If sin x + cos x = a then find the value of sin x - cos xl.​

Answer 1

Answer:

√(2-a²)

Step-by-step explanation:

Sinx + Cosx = a

Square on both sides.

=> (Sinx + Cosx)² = a²

=>Sin²x+ Cos²x + 2SinxCosx = a² (∵ Sin²x+ Cos²x = 1)

=> 1 + 2SinxCosx = a²

=> 2SinxCosx = a²-1 ----------[1]

We know that (a-b)² = (a + b)² - 4ab

(Sinx - Cosx)² = (Sinx + Cosx)² - 4 SinxCosx

                       = a² - 2* 2SinxCosx

                       = a² - 2(a² - 1)  ( from [1] )

                       = 2 - a²

Sinx - Cosx = √(2 - a²)