" 2."quad (" i) "sin^(-1)((1)/(2))-2sin^(-1)((1)/(sqrt(2)))

sin^(-1) | (1)/(sqrt (2)) |

Find the principal value of each of the following :(i)(sin^(-1)1)/(2)-2(sin^(-1)1)/(sqrt(2))( ii) sin^(-1){cos(sin^(-1)(sqrt((3)/(2)))}^(sqrt(2))

sin^-1(sqrt(3)/2) - sin^-1(1/2)

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

Show that (i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

Show that(i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

The sum of the infinte series sin^(-1)((1)/(sqrt(2)))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+...sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))