<img height="1" width="1" style="display:none" src="https://www.facebook.com/tr?id=539359806247306&ev=PageView&noscript=1"/>

Example 3 - Show (i) sin-1 (2x/root(1-x2)) = 2 sin-1 x - Formulae based


Transcript

Example 3 Show that sin-1 (2xโˆš(1 โˆ’๐‘ฅ2)) = 2 sin-1x Taking L.H.S. sin-1 ( 2x โˆš(1 โˆ’๐‘ฅ2) ) Putting x = sin ฮธ = sin-1 ("2 sin ฮธ " โˆš(1 โˆ’๐‘ ๐‘–๐‘›2" ฮธ" )) = sin-1 ("2 sin ฮธ " โˆš(๐‘๐‘œ๐‘ 2" ฮธ" )) = sin-1 (2sin ฮธ cos ฮธ) = sin-1 sin 2ฮธ = 2ฮธ = 2 ร— sin-1 x = 2 sin-1 x = R.H.S. Hence L.H.S. = R. H. S. Hence proved Example 3 Show that (ii) sin-1 (2xโˆš(1 โˆ’๐‘ฅ2)) = 2 cos-1x Taking L.H.S. sin-1 ( 2x โˆš(1 โˆ’๐‘ฅ2) ) Putting x = cos ฮธ = sin-1 ("2 cos ฮธ " โˆš(1 โˆ’๐‘๐‘œ๐‘ 2" ฮธ" )) = sin-1 ("2 cos ฮธ " โˆš(๐‘ ๐‘–๐‘›2" ฮธ" )) = sin-1 (2 cos ฮธ sin ฮธ) = sin-1 sin 2ฮธ = 2ฮธ = 2 ร— cos-1 x = 2 cos-1 x = R.H.S. Hence L.H.S. = R. H. S. Hence proved

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can contact him here.
Didn't understand? Ask your question or doubt free.

Apna sawal puchiye!

Jail