Question

solve it.....,.........

Answer 1

$sec(θ) (cos(θ) + sin(θ)) = \sqrt{2}\\ \frac{cos(θ) + sin(θ)}{cos(θ)} = \sqrt{2}\\1+\frac{sin(θ)}{cos(θ)}  = \sqrt{2}\\1+  tan(θ)= \sqrt{2}\\tan(θ)= \sqrt{2} -1$

Now we need to find out

$(2 sin(θ)) / (cos(θ) - sin(θ)) \\=\frac{2}{cot(θ) -1} \\=\frac{2tan(θ)}{1-tan(θ) } \\=\frac{2(\sqrt{2}-1) }{1-(\sqrt{2} -1) } \\=\frac{2\sqrt{2}-2 }{2-\sqrt{2}  }\\ =\frac{(2\sqrt{2}-2)*(2+ \sqrt{2}  ) }{(2-\sqrt{2}  )*(2+ \sqrt{2}  )}\\ =\frac{2\sqrt{2}}{4-2}\\\\=\sqrt{2}$

So the answer is option D

Hope it helps.!!

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