" (iii) "tan^(-1)[2cos(2sin^(-1)(1)/(2))]=(pi)/(4)

Prove that : tan^(-1) [2 cos(2sin^(-1)(1/2))] = pi/4

Prove that : tan^(-1) [2 cos(2sin^(-1)(1/2))] = pi/4

Prove that tan^(-1)1 +cos^(-1)(-(1)/(2)) +sin^(-1) (-(1)/(2)) =(3pi)/(4) .

Evaluate each of the following: sin^(-1)(sin(pi)/(3)) (ii) cos^(-1)(cos(2 pi)/(3))tan^(-1)(tan(pi)/(4))(iv)sin^(-1)(sin(2 pi)/(3))cos^(-1)(cos(7 pi)/(7))(vi)tan^(-1)(tan(3 pi)/(4))sin^(-1)(cos(-600^(@))cos^(-1)(cos(-680^(@)))

sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)-(1)/(2)(pi)/(4)=-(1)/(2)

Evaluate the following: sin^(-1)(sin(pi)/(4)) (ii) cos^(-1)(cos2(pi)/(3))tan^(-1)(tan(pi)/(3))

tan((pi)/(4) +(1)/(2)"cos"^(-1)(a)/(b))+ tan((pi)/(4) - (1)/(2)"cos"^(-1)(a)/(b)) is :

tan((pi)/(4) +(1)/(2)"cos"^(-1)(a)/(b))+ tan((pi)/(4) - (1)/(2)"cos"^(-1)(a)/(b)) is :

Prove the following: tan[(pi)/(4)+(1)/(2)cos^(-1)((a)/(b))]+tan[(pi)/(4)-(1)/(2)cos^(-1)((a)/(b))]=(2b)/(a)

tan^(-1)[sin(-pi/2)]=pi/4 .