l i m x → π 4 c o t 3 x - t a n x c o s x + π 4 is

Step-by-step solution

l i m x → π 4 c o t 3 x - t a n x c o s x + π 4 = lim x → π 4 1 tan 3 x - tan x 1 2 cos x - 1 2 sin x   ∵   cot θ = 1 tan θ = l i m x → π 4 1 - t a n 4 x t a n 3 x . 1 2 c o s x - 1 2 s i n x = lim x → π 4 1 - tan 2 x 1 + tan 2 x tan 3 x . 1 2 cos x - 1 2 sin x = l i m x → π 4 2 1 - tan x 1 + tan x sec 2 x t a n 3 x . c o s x - s i n x   ∵   1 + tan 2 x = sec 2 x   &   a 2 - b 2 = a - b a + b = lim x