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Help please; I need the right answer ​

Help please; I need the right answer ​-example-1

2 Answers

6 votes

Answer:

C

Explanation:

Given

cos x +
√(2) = - cosx ( add cosx to both sides )

2cosx +
√(2) = 0 (subtract
√(2) from both sides )

2cosx = -
√(2) ( divide both sides by 2 )

cosx = -
(√(2) )/(2)

Since cosx < 0 then x is in the second/ third quadrant

x =
cos^(-1) (
(√(2) )/(2) )

=
(\pi )/(4) ← related acute angle

Hence

x = π -
(\pi )/(4) =
(3\pi )/(4) ← second quadrant

or

x = π +
(\pi )/(4) =
(5\pi )/(4) ← third quadrant

User Guillermo
by
8.2k points
4 votes

Answer:

C.

Explanation:


\cos x+√(2)=-\cos x \\ 2\cos x = -\sqrt 2 \\ \cos x = -(\sqrt 2)/(2)\\ \\ \Rightarrow x = \pm \arccos\Big(-(\sqrt 2)/(2)\Big)+2k\pi,\quad x\in \mathbb{Z}\\ \Rightarrow x =\pm(3\pi)/(4)+2k\pi\\ \\ \\k = -1 \Rightarrow x < 0\\\\ k=0 \Rightarrow x<0 \quad \text{or}\quad \boxed{x = (3\pi)/(4)} \\ \\k = 1 \Rightarrow x=-(3\pi)/(4)+2\pi \Rightarrow \boxed{x= (5\pi)/(4)}\quad \text{or}\quad x > 2\pi

User AhmFM
by
8.8k points

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