Question

find all solutions to the equation in the interval [0, 2pi). 2 cosx +sin2x=0

Answer 1

sin(2x) or sin^2x ?

Answer 2

sin (2x)

Answer 3

\(\large\color{purple }{ \rm 2cos(x)+sin(2x)=0 }\)

\(\large\color{purple }{ \rm 2cos(x)+2sin(x)cos(x)= 0}\)

\(\large\color{purple }{ \rm 2(cos(x)+sin(x)cos(x)~~~)= 0}\)

\(\large\color{purple }{ \rm cos(x)+sin(x)cos(x)= 0}\)

Answer 4

\(\large\color{orangered }{ \rm cos(x)+sin(x)cos(x)= 0}\)
\(\large\color{orangered }{ \rm cos(x)~~(1+sin(x)~~~)= 0}\)
\(\large\color{orangered }{ \rm cos(x)= 0~~~~~or~~~~sin(x)=-1}\)

Answer 5

finish it off.

Answer 6

90 degrees and 270 degrees is the answer. Thank you!