Question

Solve (2sinx-cosx).(1+cosx)=sin²x and get the principle solution

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Answer 1

Step-by-step explanation:

Given, (2sinx−cosx)(1+cosx)=sin

2

x

⇒(2sinx−cosx)(1+cosx)−sin

2

x=0

⇒(2sinx−cosx)(1+cosx)−(1−cosx)(1+cosx)=0

⇒(1+cosx)(2sinx−1)=0

⇒1+cosx=0or2sinx−1=0

⇒cosx=−1orsinx=

2

1

⇒x=(2n+1)π,n∈Iorsinx=sin

6

π

⇒x=nπ+(−1)

n

6

π

,n∈I

∴ Solution of given equation is (2n+1)π,m∈Iornπ+(−1)

n

6

π

,n∈I