सिद्ध करें कि:
`cos^(-1)x= 2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2)), -1lexle1`

Explanation

साबित करना है कि `cos^(-1) x = 2 sin^(-1)sqrt((1-x)/(2))`
`sin^(-1)sqrt((1-x)/(2)) = theta` रखें [यहाँ `sqrt((1-x)/(2))gt0 therefore 0 le theta le(pi)/(2)]`
तो `sin theta = sqrt((1-x)/(2))rArr sin^(2)theta = (1-x)/(2)`
`rArr 1 -x = 2 sin^(2)theta rArr x = 1 - 2 sin^(2)theta`
`rArr x = cos 2theta " "rArr 2theta = cos^(1) x`
`rArr 2 sin^(-1) sqrt((1-x)/(2))=cos^(-1)x [theta` का मान रखने पर ]