" 5."tan^(-1)((2tan x)/(1-tan^(2)x))

sec^(-1)((1+tan^(2)x)/(1-tan^(2)x))

sin^(-1)((1-tan^(2)x)/(1+tan^(2)x))

sec^-1((1+tan ^2x)/(1-tan ^2 x))

sec^-1((1+tan ^2x)/(1-tan ^2 x))

Prove that: tan4x=(4tan x(1-tan^(2)x))/(1-6tan^(2)x+tan^(4)x)

cos ^(-1) ((3+5 cos x )/(5+3 cos x )) is equal to : a) tan ^(-1) ((1)/(2) tan ""(x)/(2)) b) 2 tan ^(-1) (2 tan ""(x)/(2)) c) (1)/(2) tan ^(-1) (2 tan ""(x)/(2)) d) 2 tan ^(-1) ((1)/(2) tan ""(x)/(2))

Lim_(x rarr cot^(-1)(-1))((tan^(3)x-2tan x-1)/(tan^(5)x-2tan x-1)) is equal to

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to (2x)/(1-x^2) t(2tan^(-1)x) tan(cot^(-1)(-x)-cot^(-1)(x)) "tan"(2cot^(-1)x)

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to (2x)/(1-x^2) t(2tan^(-1)x) tan(cot^(-1)(-x)-cot^(-1)(x)) "tan"(2cot^(-1)x)