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If sintheta+2costheta=1,then what is 2sintheta-costheta equal to ?

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Solution :Let`sintheta+2costheta=1` . . . (i)
Consider `2sintheta-costheta=alpha("let")`.. . (ii)
SQUARING and adding
`SIN^(2)theta+4cos^2)theta+4sinthetacostheta+4sin^(2)theta+cos^(2)theta-4sinthetacostheta=1+alpha^(2)`.
`rArr(sin^(2)theta+cos^(2)theta)+4(cos^(2)theta+sin^(2)theta)=1+alpha^(2)`.
`rArr1+4=1+alpha^(2)rArralpha^(2)=4rArralpha=2`.


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