Evaluate that : `2 arc sin (1/2) + 3 arc tan (-1) +2 arc cos (- 1/2)`

Find the value of : arc sin (1/2) + arc cos (1/2)

Evaluate the following : sin ^(2) ( cos ^(-1) . 1/2) + cos^(2) ( sin^(-1) . 1/3) .

Find the value of sin [ arc cos (- 1/2)]

The number k is such that tan { arc tan (2) + arc tan (20 k) } = k . The sum of all possible values of k is

Prove that : (cos ^(2) A + tan ^(2) A - 1 )/( sin ^(2) A ) = tan ^(2) A .

Prove that : (tan A + (1)/ (cos A))^(2) + (tan A - (1)/ (cos A))^(2) = 2 ((1 + sin^(2) A)/ (1 - sin^(2) A))

For the principal values, evaluate each of the following: (i) tan^(-1){2cos(2sin^(-1)(1/2))} , (ii) "cot"[sin^(-1){cos(tan^(-1)1)}]

For the principal values, evaluate each of the following: (i) tan^(-1){2cos(2sin^(-1)(1/2))} (ii) "cot"[sin^(-1){cos(tan^(-1)1)}]

For the principal values, evaluate each of the following: (i) tan^(-1){2cos(2sin^(-1)(1/2))} (ii) cot"[sin^(-1){cos(tan^(-1)1)}]

Evaluate : tan^(-1){2cos(2sin^(-1)""(1)/2)}