Question

Find the principal solution of sin 2x + cos x = 0.
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Answer 1

Answer:

sin2x+cosx=0

2sinxcosx+cosx=0

cosx(2sinx+1)=0

cosx=0 or 2sinx+1=0

Now, cosx=0

x=(2n+1)

2

π

,n∈Z

2sinx+1=0

sinx=−

2

1

=−sin

6

π

=sin(π+

6

π

)=sin

6

7π

x=nπ+(−1)

n

6

7π

,n∈Z

Therefore, the general solution is (2n+1)

2

π

or nπ+(−1)

n

6

7π

,n∈Z.