The Total solution for NCERT class 6-12
Given:
cos x= -3/5 and π
We know that in the third quadrant, tan x and cot xare positive and all other rations are negative.
By using the formulas,
Sin x = – √(1-cos2 x)
Tan x = sin x/cos x
Cot x = 1/tan x
Sec x = 1/cos x
Cosec x = 1/sin x
Now,
= – √(1-(-3/5)2)
= – √(1-9/25)
= – √((25-9)/25)
= – √(16/25)
= – 4/5
= (-4/5)/(-3/5)
= -4/5 × -5/3
= 4/3
= 1/(4/3)
= 3/4
= 1/(-3/5)
= -5/3
= 1/(-4/5)
= -5/4
∴ = [(-5/4) + (3/4)] / [(-5/3) – (4/3)]
= [(-5+3)/4] / [(-5-4)/3]
= [-2/4] / [-9/3]
= [-1/2] / [-3]
= 1/6