If sinx – cosx = 1, where ‘x’ is an acute angle, the

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If sinx – cosx = 1, where ‘x’ is an acute angle, the value of (sinx + cosx) is :

1. 0
2. 1
3. 1
  2
4. 2

Correct Option: B

sinx – cosx = 1 ..... (i)
sinx + cosx = y ..... (ii)
On squaring and adding both equations,
sin²x + cos²x – 2sinx.cosx + sin²x + cos²x + 2sinx . cosx
= 1 + y²
⇒ 1 + 1 = 1 + y²
⇒ y² = 1 ⇒ y = 1