sin2Xsinxcosx0 Find the range of x between 0360 degreesSolut

sin2Xsinx+cosx=0 Find the range of x between 0-360 degrees

Solution

sin2xsinx+cosx=0

=>(2sinxcosx)sinx+cosx=0

=>(2sin²xcosx)+cosx=0

=>cosx(2sin²x+1)=0

=>cosx=0, 2sin²x+1=0

=>cosx=0, sin²x=-1/2

cosx=0

=>x =90^o,270^o

sin²x=-1/2 , no solution

therefore x =90^o,270^o is the solution of sin2xsinx+cosx=0