CBSE Class 12 Math 2009 Solved Paper

Question : 1 of 29

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Using principal value, evaluate the following:

sin^{-1}(sin{3π}/5)

Solution:

sin^{-1}

(sin θ) = θ so

sin^{-1}(sin({3π}/5))

{3π}/5

But

{3π}/5

∉

[-π/2,π/2]

So,

sin^{-1}(sin({3π}/5))

sin^{-1}(sin(π-{2π}/5))

sin^{-1}(sin{2π}/5)

{2π}/5

∊

[-π/2,π/2]

∴ Principal value is

{2π}/5

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