Question 31

If $$\cot^4\theta+\cot^2\theta=3$$, then $$cosec^4\theta-cosec^2\theta=?$$

Solution

$$\cot^4\theta+\cot^2\theta=3$$

$$\cot^2\theta(Cot^2\theta+1) = 3$$.......(i)

But

$$1+ \cot^2\theta = \cosec^2\theta$$......(ii)

=> $$\cot^2\theta = \cosec^2\theta - 1$$......(iii)

From (i), (ii) and(iii)

$$(\cosec^2\theta - 1)(\cosec^2\theta) = 3$$

$$cosec^4\theta-cosec^2\theta=3$$

Hence Option (B) is right answer.

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