Well let tan x= 2.4

we know

………….sin x
tan x = ▬▬▬
………….cos x

Since sin x < 0 cos x has to be less
than 0 too for the tangent ratio to be
positive

so sin x = 2.4 cos x

thus, using the identity

sin² x + cos² x = 1

we substitute

(2.4 cos x)² + (cos x)² = 1

5.76 cos² x + 1 cos² x = 1

6.76 cos² x = 1

consequently

……………1
cos² x = ▬▬▬
………….6.76

thus cos x = -(1/√6.76)) = -1/2.6 = -10/26 = -5/13