If x is in the third quadrant, then
a) Choose the possible values of cosec x from the bracket. {-3/5 ,3/5 ,5/3, -5/3 }
b)Evaluate tan x sec x for the x in part (a)

Question

If x is in the third quadrant, then
a) Choose the possible values of cosec x from the bracket {-3/5
,3/5 ,5/3, -5/3 }
b)Evaluate tan x sec x for the x in part (a)

Vivek Rai · Accepted Answer

As x is in third quadrant, where CosecX is a negative quantity
Also
CosecX∈(-∞,-1]∪[1,∞) so out of the options available, cosecX can only be equal to -53Now, if CosecX=-53, we have sinx=-35⇒cosX=-1--352=-45, As cosX is also negative in third Quadrant
 and cosX=±1-sin2xwe have to find the value of secX
tanX=1cosX SinXCosX=-35-452=-1516
Hope this clears your doubt
With regards

If x is in the third quadrant, then a) Choose the possible values of cosec x from the bracket. {-3/5 ,3/5 ,5/3, -5/3 } b)Evaluate tan x sec x for the x in part (a)

If x is in the third quadrant, then
a) Choose the possible values of cosec x from the bracket. {-3/5 ,3/5 ,5/3, -5/3 }
b)Evaluate tan x sec x for the x in part (a)