Question

If cot theeta = 8/15 then find the value of cosec theeta and sec theeta​

Answer 1

The value of cosec theta and sec theta are 17/15 & 17/8 respectively.

Step-by-step explanation:

Let’s assume a right-angled triangle ABC with B = 90°.

Considering the trigonometry properties for triangle ABC, we know that,      

cot θ = 1/tanθ = [Base] / [Perpendicular] = BC/AB

cosec θ = 1/sinθ = [Hypotenuse] / [Perpendicular] = AC/AB ….. (i)

sec θ = 1/cosθ = [Hypotenuse] / [Base] = AC/BC ….. (ii)

Here, we are given the value of,

cot θ = 8/15 i.e., BC = 8 & AB = 15

Now, applying Pythagoras theorem in ∆ABC, we have

Base² + perpendicular² = Hypotenuse²

 

⇒ BC² + AB² = AC²

⇒ 8² + 15² = AC²

⇒ AC = √[64 + 225]

⇒ AC = 17

Thus, substituting the values of AB, BC & AC in eq. (i) & (ii), we get

The value of,

cosec θ = AC/AB = 17 / 15

and,

sec θ =  AC/BC = 17 / 8

Hope this is helpful!!!!

Answer 2

if cot θ = 8/15 then Cosecθ = ± 17/15   & Secθ  =  ± 17/8

Step-by-step explanation:

cot θ = 8/15

=> Cosθ /Sinθ = 8/15

Let say Cosθ = 8k   Then Sinθ = 15k

as we know that

Cos²θ + Sin²θ = 1

=> (8k)²  + (15k)² = 1

=> 64k² + 225k² = 1

=> 289k² = 1

=> k² = 1/289

=> k = ± 1/17

Cosθ  = 8k  = ± 8/17  => Secθ  = 1/Cosθ  =  ± 17/8

Sinθ  = 15k  = ± 15/17  => Cosecθ  = 1/Sinθ   =  ± 17/15

Cosecθ = ± 17/15

Secθ  =  ± 17/8