Question

if cos x =5/13 and x is acute find the value of tan x + cot x ÷ tan x - cot x

Answer 1

We can solve it by thinking geometrically.

Cosx=5/13, as you know that cos x=base/hypotenuse So, we can apply it over here.

Cosx=5/13=base/hypotenuse

So, base=5, hypotenuse=13

(Not taking any constant, as it'll get cancelled)

By applying Pythagoras theorem we get

Perpendicular=√H^2-b^2

=√13^2-5^2

=√169-25. =√144. =12

P=12

Tanx=12/5(P/B). Cotx=5/12(B/P)

Tanx+Cotx/Tanx-Cotx

12/5+5/12÷12/5-5/12

169/60÷129/60

=169/129

Hope you understood!!