E-sin2x-cosx-sinx-1-2-1-show-that-E-is-equivalent-to-E-2cos-2-X-2-cosX-1-2-0-with-X-x-pi-4-

Question Number 81003 by mathocean1 last updated on 08/Feb/20

(E) : \sin 2 x = c o s x + s i n x - \frac{1}{2}

1 . s h o w t h a t (E) is equivalent to

(E^{'}) : {2 \cos}^{2} X - \sqrt{2} cosX - \frac{1}{2} = 0

with X = x - \frac{π}{4} .

Commented by MJS last updated on 08/Feb/20

wrong

Commented by mathocean1 last updated on 09/Feb/20

how sir ?

Commented by jagoll last updated on 09/Feb/20

\sin x + \cos x - \frac{1}{2} = \sqrt{2} \cos (x - \frac{π}{4}) - \frac{1}{2}

= \sqrt{2} \cos X - \frac{1}{2}

n o w \sin 2 x = 1 + 2 \sin x \cos x - 1

{(\sin x + \cos x)}^{2} - 1 = {(\sqrt{2} \cos X)}^{2} - 1

s o E \Rightarrow 2 \cos^{2} X - 1 = \sqrt{2} \cos X - \frac{1}{2}

2 \cos^{2} X - \sqrt{2} \cos X - \frac{1}{2} = 0

Commented by MJS last updated on 09/Feb/20

haha I cannot subtract correctly anymore \dots

time for the primary school again

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