(1) `4(tan^(-1)(1)/(3)+cos^(-1)(2)/(sqrt(5)))`

Find the principal value of the following cos e c^(-1)(2) (ii) tan^(-1)(-sqrt(3)) cos^(-1)(1/(sqrt(2)))

Prove that tan ^(-1) ""(1)/(4) + tan ^(-1) ""(2)/(9) = cos ^(-1) ((2)/(sqrt5))

The value of 3 "tan"^(-1)(1)/(2) + 2 "tan"^(-1)(1)/(5) + "sin"^(-1)(142)/(65sqrt(5)) is :

Find the value of expression: sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2))

Find the value of expression: sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2))

Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/sqrt(5))

Find the value of expression: sin(2tan^(-1)1/3)+cos(tan^(-1)2sqrt(2))

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Evaluate the following:(i) sin(1/2\ cos^(-1)(4/5)) (ii) sin(2\ tan^(-1)(2/3))+cos(tan^(-1)sqrt(3))

Which of the following is not a rational number. a. sin (tan^(-1) 3 + tan^(-1).(1)/(3)) b. cos ((pi)/(2) - sin^(-1).(3)/(4)) c. tan ((1)/(2) cos^(-1).(sqrt5)/(3))