Question

If sinθ-cosθ=1/2,
then find the value of
1/sinθ+ cosθ​​

Answer 1

$\Huge\bf\maltese{\underline{\green{Answer°᭄}}}\maltese$

$\implies$$\large\bf{\underline{\red{VERIFIED✔}}}$

$sin θ - cos θ = \frac{1}{2} \\ On \: squaring \: both \: sides,  \\ (sin θ - cos θ \ {)}^{2}  = ( \frac{1}{2} {)}^{2} \\ \sin^{2} θ + co {s}^{2} θ - 2sin \: θ \cosθ = \frac{1}{4} \\ 1 - 2sin \: θ \: cos \: θ = \frac{1}{4} \\ 2sin \: θ \: cos \: θ = 1 - \frac{1}{4} = \frac{3}{4} \\ (sin θ + cosθ {)}^{2} = si {n}^{2} θ + co {s}^{2} θ + 2sinθ\: cosθ \\ = 1 + 2sin θcos θ \\ = 1 + \frac{3}{4} = \frac{7}{4} \\ sin θ + cos θ = √( \frac{7}{4} ) = √ \frac{7}{4}$

$\boxed{I \:Hope\: it's \:Helpful}$