Login

Show that sin^-11/ root 5 + sin ^-12 /root 5 = pi/2

LHS = \sin^{- 1} (\frac{1}{\sqrt{5}}) + \sin^{- 1} (\frac{2}{\sqrt{5}}) = \sin^{- 1} [\frac{1}{\sqrt{5}} \sqrt{1 - {(\frac{2}{\sqrt{5}})}^{2}} + \frac{2}{\sqrt{5}} \sqrt{1 - {(\frac{1}{\sqrt{5}})}^{2}}] = \sin^{- 1} [\frac{1}{\sqrt{5}} \sqrt{1 - \frac{4}{5}} + \frac{2}{\sqrt{5}} \sqrt{1 - \frac{1}{5}}] = \sin^{- 1} [\frac{1}{\sqrt{5}} \times \frac{1}{\sqrt{5}} + \frac{2}{\sqrt{5}} \times \frac{2}{\sqrt{5}}] = \sin^{- 1} [\frac{1}{5} + \frac{4}{5}] = \sin^{- 1} [\frac{5}{5}] = \sin^{- 1} (1) = \sin^{- 1} [\sin (\frac{π}{2})] = \frac{π}{2} = RHS Using : \sin^{- 1} x + \sin^{- 1} y = \sin^{- 1} [x \sqrt{1 - y^{2}} + y \sqrt{1 - x^{2}}]

-2

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?