# 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.

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.

## Recent Articles 1. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 01, 23 01:16 AM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

2. ### Days of the Week | 7 Days of the Week | What are the Seven Days?

Nov 30, 23 10:59 PM

We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…