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Question
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cosec C = `sqrt(10)`
Solution
cosec C = `sqrt(10)`
cosec C = `(1)/"sin C" = "Hypotenuse"/"Perpendicular" = sqrt(10)/(1)`
By Pythagoras theorem, we have
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ Base = `sqrt(("Hypotenuse")^2 - ("Perpendicular")^2`
⇒ Base
= `sqrt((sqrt(10))^2 - (1)^2`
= `sqrt(10 - 1)`
= `sqrt(9)`
= 3
sin C = `"Perpendicular"/"Hypotenuse" = (1)/sqrt(10)`
cos C = `"Base"/"Hypotenuse" = (3)/sqrt(10)`
tan C = `"Perpendicular"/"Base" = (1)/(3)`
sec C =`(1)/"cos C" = sqrt(10)/(3)`
cot C = `(1)/"tan A"` = 3.
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