Trigonometry-sin-2x-5-sin-x-cos-x-1-0-find-the-solution-

Question Number 135594 by liberty last updated on 14/Mar/21

T r i g o n o m e t r y

\sin 2 x + 5 (\sin x + \cos x) + 1 = 0

f i n d t h e s o l u t i o n

Answered by EDWIN88 last updated on 14/Mar/21

let \sin x + \cos x = E then 1 + \sin 2 x = E^{2}

the equation becomes

E^{2} - 1 + 5 E - 1 = 0 \Rightarrow {\begin{cases} E = 0 \\ E = - 5 (rejected) \end{cases}

from E = 0 \Rightarrow \tan x + 1 = 0 so we get the

solution is x = - \frac{π}{4} + n π, n \in Z

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