1.

Prove that : `tantheta+tantheta+tan(90^(@)-theta)=sectheta*sec(90^(@)-theta)`

Answer» L.H.S. `=tantheta+tan(90^(@)-theta)`
`=tantheta+cottheta`
`=(sintheta)/(costheta)+(costheta)/(sintheta)=(sin^(2)theta+cos^(2)theta)/(costhetasintheta)`
`=(1)/(costheta*sintheta)=sectheta*"cosec "theta`
`=sectheta*sec(90^(@)-theta)=R.H.S.`


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