prove-that-sin-x-cos-x-2-cos-x-pi-4-

Question Number 105892 by mohammad17 last updated on 01/Aug/20

p r o v e t h a t s i n (x) + c o s (x) = \sqrt{2} c o s (x - \frac{π}{4}) ?

Answered by john santu last updated on 01/Aug/20

\sin x + \cos x = p

\frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x = \frac{p}{\sqrt{2}}

\Rightarrow \sin (\frac{π}{4}) \sin x + \cos (\frac{π}{4}) \cos x

= \frac{p}{\sqrt{2}}

(r e c a l l : \cos t \cos h + \sin t \sin h

= \cos (t - h))

\Leftrightarrow \cos (x - \frac{π}{4}) = \frac{p}{\sqrt{2}}

p = \sqrt{2} \cos (x - \frac{π}{4}) .

p r o v e d .

Commented by mohammad17 last updated on 01/Aug/20

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