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Find the general solution of equation: sin(x/2) = 0

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11th

Maths

Trigonometric Functions

Trigonometric Equations

Find the GENERAL SOLUTION o...

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Find the general solution of the EQUATION sin2x+cosx=0.

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ANSWER

sin2x+cosx=0

2sinxcosx+cosx=0

cosx(2sinx+1)=0

cosx=0 or 2sinx+1=0

Now, cosx=0

x=(2n+1)2π,n∈Z

2sinx+1=0

sinx=−21=−sin6π=sin(π+6π)=sin67π

x=nπ+(−1)n67π,n∈Z

Therefore, the general solution is (2n+1)2π or nπ+(−1)n

Step-by-step explanation:

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