L=1−cosx−2sin2x
PutL=0 in L=1−cosx−2sin2x,we get
⇒1−cosx−2sin2x=0
⇒1−cosx−2(1−cos2x)=0 [∵sin2x+cos2x=1]⇒1−cosx−2+2cos2x=0
⇒2cos2x−cosx−1=0⇒2cos2x−2cosx+cosx−1=0
⇒2cosx(cosx−1)+(cosx−1)=0⇒(cosx−1)(2cosx+1)=0⇒cosx−1=0or2cosx+1=0
⇒cosx=1 or 2cosx=−1⇒cosx=1 or cosx=−1/2⇒x=360∘norx=120∘+360∘n or x=240∘+360∘n,n∈Z
Hence the values of x for which the water level is zero are,
x=360∘n or x=120∘+360∘n or x=240∘+360∘n,n∈Z
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