solve-in-R-sin-piln-x-cos-piln-x-1-

Question Number 83473 by M±th+et£s last updated on 02/Mar/20

s o l v e i n R

s i n (π l n (x)) + c o s (π l n (x)) = 1

Answered by mind is power last updated on 02/Mar/20

\Rightarrow \frac{\sqrt{2}}{2} s i n (π l n (x)) + \frac{\sqrt{2}}{2} c o s (π l n (x)) = \frac{1}{\sqrt{2}}

\Rightarrow s i n (π l n (x) + \frac{π}{4}) = \frac{1}{\sqrt{2}}

\Rightarrow π l n (x) + \frac{π}{4} = \frac{π}{4} + 2 k π \lor \frac{3 π}{4} + 2 k π

\Rightarrow x = e^{2 k} \lor x = e^{\frac{1}{2} + 2 k}, k \in Z

Commented by M±th+et£s last updated on 02/Mar/20

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