Question

if cos x = -3/5 and pi less tha x , x less tha 3pi/2, find the other trignometric ratios and hence evaluate : cosec x + cot x/sec x - tan x

Answer 1

cos(53)=3/5
since x lies between 180 and 270 degree
x=pi+53
(cos(pi+a)= -cos(a)) (angle conversion)
hence value of x is (pi+53)
cosec(x)=cosec(pi+53)= -cosec(53) = -5/4
(since value of sin(53)=4/5)
similarly
cot(x)=4/3
sec(x)= -5/3
tan(x)=3/4
by substituting the values we get the answer as (-14/5)