`cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x)/(2)-cos^(-1)x`

cos^(-1)((x^(2))/(6)+sqrt(1-(x^(2))/(9))sqrt(1-(x^(2))/(4)))=cos^(-1)((x)/(3))-cos^(-1)((x)/(2)) hold for all x belonging to

cos^(-1)sqrt((sqrt(1+x^(2))+1)/(2sqrt(1+x^(2))))

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=(pi)/(4)+(1)/(2)cos^(-1)x^(2)

Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2)

3cos^(-1)x=sin^(-1)(sqrt(1-x^(2))(4x^(2)-1))

cos^(-1){(x)/(sqrt(x^(2)+a^(2))))

cos^(-1)((sqrt(1+x)-sqrt(1-x))/(2))

cos^(-1)((2sqrt(x))/(1+x))