Question

plz answer this qstn​

Answer 1

Given,

$\sin - \cos = \frac{1}{2}$

Solution:-

$(sin - cos) {}^{2} +( sin + cos) {}^{2} \\ = > {sin}^{2} + {cos}^{2} - 2sincos + {sin}^{2} + {cos}^{2} + 2sin \times cos \\ = > 2( { {sin}^{2} } + {cos}^{2} ) \\ = > 2$

$(sin - cos) {}^{2} +( sin + cos) {}^{2} = 2 \\ = > putting \: sin - cos = \frac{1}{2} \\ \\ = > ( \frac{1}{2}) {}^{2} + (sin + cos) {}^{2} = 2 \\ \\ = > \frac{1}{4} + (sin + cos) {}^{2} = 2 \\ \\ = > (sin + cos) {}^{2} = 2 - \frac{1}{4} \\ = > (sin + cos) {}^{2} = \frac{8 - 1}{4} \\ = > (sin + cos) {}^{2} = \frac{7}{4} \\ = > (sin + cos) = \frac{ \sqrt{7} }{2}$

Answer 2

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