Prove that:
`tan(pi/3-A).tan(pi/3+A)= (2cos2A+1)/(2cos2A-1)`

Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

Prove that : tan^2 (pi/4)+tan^2(pi/4)+tan^2(pi/3)=13/3

Prove that : tan^(-1)2+tan^(-1)3=(3 pi)/(4)

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

Prove that: (cos2A)/(1+sin2A) = tan(pi/4-A)

Prove that: tan^(-1){(pi)/(4)+(1)/(2)(cos^(-1)a)/(b)}+tan{(pi)/(4)-(1)/(2)(cos^(-1)a)/(b)}=(2b)/(a)

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

Prove that (1+sin2A)/(cos2A)=(cos A+sin A)/(cos A-sin A)=tan((pi)/(4)+A)

prove that tan ((pi) / (4) + (1) / (2) cos ^ (- 1) ((a) / (b))) + tan ((pi) / (4) - (1) / (2) cos ^ (- 1) ((a) / (b))) = (b) / (a) cos ^ (- 1) ((cos x + cos y) / (1 + cos x cos y) ) = 2tan ^ (- 1) ((tan x) / (2) (tan y) / (2))