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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 : |
$\frac{2}{3}$ $\frac{1}{3}$ $-\frac{1}{3}$ $-\frac{2}{3}$ |
$\frac{1}{3}$ |
cosec²θ - cot²θ = 1 & cosec²θ+ cot²θ = \(\frac{1}{3}\) Now, cosec4 θ- cot2 θ = ( cosec²θ - cot²θ ) . ( cosec²θ+ cot²θ ) = 1 . \(\frac{1}{3}\) = \(\frac{1}{3}\) |
