1.

The number of solutions of equation `tanx+secx=2cosx` lying in the interval `[0, 2pi]` is

Answer» Correct Answer - C
Given equation, `" "tanx+secx=2cosx`
`rArr" "(sinx)/(cosx)+(1)/(cosx)=2cosx`
`rArr" "1+sinx=2cos^(2)x`
`rArr" " 1+sinx=2(1-sin^(2)x)`
`rArr" "1+sinx=2-2sin^(2)x`
`rArr" "2sin^(2)x+sinx-1=0`
`rArr" "2sin^(2)x+sinx-1=0`
`rArr" "2sinx(sinx+1)-1(sinx+1)=0`
`rArr" "(sinx+1)(2sinx-1)=0`
`rArr" "sinx+1=0 or (2sinx-1)=0`
`rArr" "sinx=-1, sinx=(1)/(2)`
`therefore" "x=(3pi)/(2), x= (pi)/(6)`
Hence, only two solutions possible.


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