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

From arcsec x + arccsc x = π/2 to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?