1.

मूल्यांकन कीजिए - `tan^(-1)(sqrt3)-sec^(-1)(-2)+"cosec"^(-1)((2)/(sqrt3))`.

Answer» `tan^(-1)(sqrt3)=(pi)/(3)" "`[उदाहरण 1 (iii ) से]
`sec^(-1)(-2)=(2pi)/(3)" "` [उदाहरण 2 (iv ) से ]
माना `"cosec"^(-1)((2)/(sqrt3))=theta`
`rArr" cosec"theta =(2)/(sqrt3)." "theta in [-(pi)/(2),(pi)/(2)]-{0}`
`rArr" cosec"theta="cosec"(pi)/(3)`
`rArr" "theta=(pi)/(3) "cosec" [-(pi)/(2),(pi)/(2)]-{0}`
`therefore tan^(-1)sqrt3-sec^(-1)(-2)+"cosec"^(-1)((2)/(sqrt3))`
`=(pi)/(3)-(2pi)/(3)+(pi)/(3)`
= 0.


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