Question

cosec theta+cot theta=root 3 what is the answer of cosec theta and cot theta

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

Trigonometry is the study of angles and its ratios. This study prescribes the relation amongst the sides of a triangle and angles of the triangle.

There are sine, cosine, tangent, cot, sectant and cosec ratios to an angle of a triangle.

Let me tell you an interesting fact about Trigonometry.

"Triangle" > "Trigonometry"

Remember some formulae now :

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1

Want to learn more!

Here it is :

sin(A + B) = sinA cosB + cosA sinB

sin(A - B) = sinA cosB - cosA sinB

cos(A + B) = cosA cosB - sinA sinB

cos(A - B) = cosA cosB + sinA sinB

♤SOLUTION♤

Given :

cosecθ + cotθ = √3 .....(i)

We know that :

cosec²θ - cot²θ = 1

=> (cosecθ + cotθ)(coseθ -cotθ) = 1

=> √3(cosecθ - cotθ) = 1

=> cosecθ - cotθ = 1/√3 .....(ii)

Now, adding (i) and (ii), we get :

2cosecθ = √3 + 1/√3 = (3 + 1)/√3 = 4/√3

=> cosecθ = 2/√3

From (i), putting cosecθ = 2/√3, we get :

cotθ = cosecθ - √3

=> cotθ = √3 - 2/√3 = (3 - 2)/√3

=> cotθ = 1/√3

Therefore, the required answer is :

cosecθ = 2/√3 and cotθ = 1/√3.

♧♧HOPE THIS HELPS YOU♧♧