cot x=3/4,x lies in third quadrant

1.	cot x=3/4,x lies in third quadrant
Answer» cot x = 3/4 (given) We know that in the third quadrant only tan and cot can remains positive. Therefore tan x = 1/cotx = 1/3/4 =4/3 We know that 1 + tan^2x = sec^2x ⇒ 1 + (4/3)^2= sec^2x ⇒ 1 + 16/9 = sec^2x = 9+16/9 = 25/9 sec^2x = 25/9 or sec x = +- 5/3 since x lies in the third quadrant thereforesec x = -5/3 We know that sec x = 1/cos x ⇒ -5/3 = 1/ cosx ⇒ cosx = 1/-5/3 orcos x =-3/5 We know that sinx = perpendicular / Hypotenuse ⇒sin x = -4/5 Therefore cosec x = 1 / sinx = -5/4 cosec x = -5/4

Answer»

cot x = 3/4 (given)

We know that in the third quadrant only tan and cot can remains positive.

Therefore tan x = 1/cotx = 1/3/4 =4/3

We know that 1 + tan^2x = sec^2x

⇒ 1 + (4/3)^2= sec^2x

⇒ 1 + 16/9 = sec^2x = 9+16/9 = 25/9

sec^2x = 25/9 or sec x = +- 5/3

since x lies in the third quadrant thereforesec x = -5/3

We know that sec x = 1/cos x ⇒ -5/3 = 1/ cosx

⇒ cosx = 1/-5/3 orcos x =-3/5

We know that sinx = perpendicular / Hypotenuse

⇒sin x = -4/5

Therefore cosec x = 1 / sinx = -5/4

cosec x = -5/4

Discussion