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If cottheta +tantheta= 2"cosec"theta, th...

If `cottheta +tantheta= 2"cosec"theta`, then find the general value of `theta`.

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Given that, `" "cottheta+tan theta=2"cosec"theta`
`rArr" "(costheta)/(sintheta)+( sintheta)/(costheta)=(2)/(sintheta)`
`rArr" "(cos^(2)+sin^(2)theta)/(sintheta *costheta)=(2)/(sintheta) `
`rArr" "(1 )/(costheta)=2" "` `[becausesin^(2 )theta+cos^(2)theta=1]`
`therefore" "costheta=(1)/(2) rArrcostheta=cos""(pi)/(3)`
`therefore" "theta=2npipm(pi)/(3)`
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