If sinθ+ cosecθ=2, then the value of $$sin^{-7}θ + cosec^7θ$$ is
$$sin \theta + \dfrac{1}{sin \theta} = 2$$
$$sin^2 \theta + 1 = 2sin\theta$$
$$sin^2 \theta -2sin\theta+1=0$$
$$(sin\theta-1)^2 = 0$$
$$sin\theta=1$$
=> $$\theta = 90^\circ$$
Substituting $$\theta$$ = 90$$^\circ$$
Then, $$sin^{-7}\theta + cosec^7\theta = 1^{-7} + 1^7 = 1+1 = 2$$
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