Question

If cotθ=1/√3, find the value of 1-cos²θ/2-sin²θ

Answer 1

Answer:

hey mate:-

Step-by-step explanation:

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.

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Answer 2

cot (theta) = 1/ root (3)

cos^2 (60) = 1/4

sin^2 (60) = 3/4

(3/4)/(5/4)= 3/5