If $ cosec^2 θ + cot^2 θ = \frac{1}{3},$ where $0 ≤ θ ≤ \frac{π}{2}$, then the value of $cosec^4θ - cot^4 θ$ is :
Answer & explanation
Correct answer: option 2
cosec²θ - cot²θ = 1
& cosec²θ+ cot²θ = \(\frac{1}{3}\)
Now,
cosec4 θ- cot2 θ = ( cosec²θ - cot²θ ) . ( cosec²θ+ cot²θ )
= 1 . \(\frac{1}{3}\)
= \(\frac{1}{3}\)