# Suppose a and b are numbers such that `cos^-1a=pi/7 and sin^-1b=pi/7` `` Explain why `a^2+b^2=1` ``

*print*Print*list*Cite

Expert Answers

hala718 | Certified Educator

`cos^-1 a = pi/7 `

`==gt cos(cos^-1 a) = cos(pi/7)`

==> a = cos(PI/7) ............(1)

`sin^-1 b = pi/7 `

`==gt sin(sin^-1 b) = sin(pi/7) `

`==gt b = sin(pi/7) ............(2)`

`` Now we know that:

`sin^2 x + cos^2 x = 1 `

`==gt sin^2 (pi/7) + cos^2 (pi/7) = 1`

```==gt b^2 + a^2 = 1`

``