Question

if cos-sin=x ans sin+cos=y then show x ²+y²=2​

Answer 1

(cos -sin )² = x²

x² = cos² - 2cos.sin + sin ²

y² = (sin + cos)²

= sin² + 2sin.cos + cos²

But sin² + cos² = 1

So, x² = 1 - 2sin.cos

y² = 1+ 2sin.cos

L.H.S. = x² + y²

= 1 - 2sin.cos + 1 + 2sin.cos

= 2

R.H.S. = 2

L.H.S = R.H.S

Hence proved

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Answer 2

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