Question

"Question5
If cosec θ=√10,Find the vvalues of all T-ratios of θ.
Chapter 5 , Trigonometry, Exercise -5 , Page number - 273"

Answer 1

Hey there!
We know that,
cosecθ = Hypotenuse / Opposite side to theta
cosecθ = √10 / 1

Hypotenuse = √10
Opposite side = 1

By Pythagoras theorem,
( Hypotenuse )² = (Adjacent side) ²+ (Opposite side) ²

Adjacent side = √[ ( √10)² - 1² ] = √9 = 3

Now, Trigonometry ratios :

cosθ = Adjacent side to theta / Hypotenuse = 3/√10

sinθ = Opposite side of theta / Hypotenuse = 1/√10

tanθ = sinθ/cosθ = 1/3
cotθ = 1/tanθ = 1/( 1/3) = 3
secθ = 1/cosθ = 1/(3/√10) = √10/3


∴ The trigonometric ratios , cosθ = 3/√10 , sinθ = 1/√10 , tanθ = 1/3 , cotθ = 3 , secθ = √10/3

Answer 2

I hope this will help you


-by ABHAY