Question

Prove that tanx + cotx=2cosec2x and deduce that tan75 + cot75=4.

Answer 1

tan x + cot x = sinx /cos x + cos x /sin x
=( sin²x + cos²x) /sinx cos x
= 2 / 2sinx cos x
= 2/sin 2x
= 2 cosec 2x
tan 75 + cot 75 =2 cosec 150 = 2 × 2 = 4

Answer 2

Answer:

Step-by-step explanation:

LHS = tan(x) + 1/tan(x) = { [tan(x)]^2 + 1}/tan(x)

= [sec(x)]^2 /tan(x) = 1 /sin(x)cos(x) = 2 /sin(2x) = 2*cosec(2x) = RHS

tan(75) + cot(75) = 2*cosec(150) = 2 /sin(150) = 2 /sin(30) = 4