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Question
If 5 cot θ = 12, find the value of : Cosec θ+ sec θ
Solution
Consider the diagram below :
5cot θ = 12
cot θ = `(12)/(5)`
i.e.`"base"/"perpendicular" = (12)/(5)`
Therefore if length of base = 12x, length of perpendicular = 5x
Since
base2 + perpendicular2 = hypotenuse2 ...[ Using Pythagoras Theorem]
(12x)2 + (5x)2 = hypotenuse2
hypotenuse2 = 144x2 + 25x2 = 169x2
∴ hypotenuse = 13x
Now
cosec θ = `"hypotenuse"/"perpendicular" = (13x)/(5x) = (13)/(5)`
sec θ = `"hypotenuse"/"base" = (13x)/(12x) = (13)/(12)`
Therefore
cosec θ+sec θ
= `(13)/(5)+(13)/(12)`
= `(221)/(60)`
= `3(41)/(60)`
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