Question

If sinx+cosx=a then |sinx-cosx|​

Answer 1

Answer:

sinx+cosx=a

Now, (sinx+cosx)2+(sinx−cosx)2=2

⇒a2+(sinx−cosx)2=2

⇒(sinx−cosx)2=2−a2

⇒sinx−cosx=±2−a2−−−−−√

Hence, |sinx−cosx|=2−a2−−−−−√

Answer 2

Answer:

sinx + cosx = a

squaring both sides

sin²x + cos²x +2sinxcosx = a²

2sinxcosx = a² - 1

(sinx - cosx )² = sin²x + cos²x - 2sinxcosx = 1 - (a² - 1) = 2-a²

|sinx-cosx| = √(2-a²)

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