" 6.1.3"cosec^(-1)(sqrt(2))

Find the values of : (1) cos^(-1)((1)/(2))+tan^(-1)((1)/sqrt(3)) (2) cos^(-1)((1)/(2))+2sin^(-1) ((1)/(2)) (3) cosec ^(-1)(-sqrt(2))+cot^(-1)(sqrt(3)) .

Find the principal value of: i) sin^(-1)(sqrt(3)/2) ii) sin^(-1)(1/2) iii) cos^(-1)(1/2) iv) tan^(-1)(1) v) tan^(-1)(1/sqrt(3)) vi) sec^(-1)(2/sqrt(3)) , vii) "cosec"^(-1)(sqrt(2)) .

Find the principal value of: i) sin^(-1)(-1/sqrt(2)) , ii) cos^(-1)(-sqrt(3)/2) iii) tan^(-1)(-sqrt(3)) iv) sec^(-1)(-2) v) "cosec"^(-1)(-sqrt(2)) , vii) cot^(-1)(-1/sqrt(3)) .

The prinicipal value of "cosec"^(-1)(-sqrt(2)) is -

The principal value of "cosec"^(-1)(-sqrt(2)) is

(tan ^(-1) (sqrt(3))-sec ^(-1)(-2))/("cosec"^(-1)(-sqrt(2))+cos^(-1)""(-(1)/(2)))=

sec^(2)cot ^(-1)""((1)/(sqrt(3)))+tan^(2)"cosec"^(-1) (sqrt(2))

Find the principal values of the following : (i) sin ^(-1) ((-sqrt(3))/(2)) (ii) cot^(-1)sqrt(-3) (iii) cos^(-1)(-(1)/(2)) (iv) cosec^(-1)(sqrt(2)) (v) tan^(-1) (vi) cosec^(-1)(-1)