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arcsec(x) + arccsc(x) = \frac{π}{2}

We will learn how to prove the property of the inverse trigonometric function arcsec(x) + arccsc(x) = \frac{π}{2} (i.e., sec^{-1} x + csc^{-1} x = \frac{π}{2}).

Proof: Let, sec^{-1} x = θ              

Therefore, x = sec θ

x = csc (\frac{π}{2} - θ), [Since, csc (\frac{π}{2} - θ) = sec θ]

⇒ csc^{-1} x = \frac{π}{2} - θ

⇒ csc^{-1} x= \frac{π}{2} - sec^{-1} x, [Since, θ = sec^{-1} x]

⇒ csc^{-1} x + sec^{-1} x = \frac{π}{2}

⇒ sec^{-1} x + csc^{-1} x = \frac{π}{2}

Therefore, sec^{-1} x + csc^{-1} x = \frac{π}{2}.         Proved.






















11 and 12 Grade Math

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