1.

If `"cosec"x=1+cotx`, then `x=2npi,2npi+(pi)/(2)`

Answer» True
Given that, `" ""cosec"x=1+cotx`
`rArr" "(1)/(sinx)=1+(cosx)/(sinx)rArr(1)/(sinx)=(sinx+cosx)/(sinx)`
`rArr" "sinx+cosx=1`
`rArr" "(1)/(sqrt(2))*sinx+(1)/(sqrt(2))*cosx=(1)/(sqrt(2))`
`rArr" "sin""(pi)/(4)sinx+cosxcos""(pi)/(4)=(1)/(sqrt(2))`
`rArr" "cos(x-(pi)/(4))=cos""(pi)/(4)`
`therefore" "x-(pi)/(4)=2npipm(pi)/(4)`
For positive sign, `" "x=2npi+(pi)/(4)+(pi)/(4)=2npi+(pi)/(2)`
For negative sign, `" "x=2npi-(pi)/(4)+(pi)/(4)=2npi`


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