Question 143

If sin θ + cosec θ = 2 then the value of $$sin^{5}θ + cosec^{5} θ$$ is

Solution

Expression : $$sin \theta + cosec \theta = 2$$

=> $$sin \theta + \frac{1}{sin \theta} = 2$$

=> $$sin^2 \theta - 2sin \theta + 1 = 0$$

=> $$(sin \theta -1)^2 = 0$$

=> $$sin \theta = 1$$

and $$cosec \theta = 1$$

$$\therefore sin^5 \theta +cosec^5 \theta = 1 + 1 = 2$$

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