Question

if sin theta + cos theta= p then sin theta-cos theta is​

Answer 1

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Given :-

sinθ + cosθ = p

To find :-

The value of sinθ - cosθ

Identity used :-

$\ \fcolorbox{black}{cyan}{♛sin²θ + cos²θ = 1♛}$

Solution:-

Consider

(sinθ + cosθ)² + (sinθ - cosθ)²

= sin²θ + cos²θ + 2 × sinθ × cosθ + sin²θ + cos²θ - 2 × sinθ × cosθ

= 1 + 1

= 2

=> (sinθ + cosθ)² + (sinθ - cosθ)² = 2

=> p² + (sinθ - cosθ)² = 2

=> (sinθ - cosθ)² = 2 - p²

$\large\bold\red{ = > \: (sinθ - cosθ) = \sqrt{2 - {p}^{2} } }</p><p>$

$\huge \fcolorbox{black}{m}{♛Hope it helps U♛}$