Question

2cos^2x-1=0

find all solutions (there can be more than 1)

pi/8
-7pi/4
15pi/4
3pi/4

Answer 1

\(\Large\color{blue}{ \bf 2cos^2x-1=0 }\)
\(\Large\color{blue}{ \bf 2cos^2x=1 }\)
\(\Large\color{blue}{ \bf cos^2x=1/2 }\)
\(\Large\color{blue}{ \bf cosx=1/4 }\)

Answer 2

2 * cos² x - 1 = 0

<=>

2 * cos² x = 1

<=>

cos² x = 1/2

<=>

cos x = - sqr (1/2) or cos x = sqr (1/2)

<=>

cos x = - sqr (2) / 2 or cos x = sqr (2) / 2

<=>

x = 3pi/4 or x = 5pi/4 or x = 7pi/4 or x = pi/4


Answers :

pi/4 ; 3pi/4 ; 5pi/4 ; 7pi/4 ===> radians

45 ; 135 ; 225 ; 315 ===> degrees

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