Question 58

If $$cosec^{4}A - cosec^{2}A = x$$, then value of x is?

Solution

Expression : $$cosec^{4}A - cosec^{2}A = x$$

= $$cosec^2A(cosec^2A - 1)$$

= $$cosec^2A(\frac{1}{sin^2A} - 1)$$

= $$cosec^2A(\frac{1-sin^2A}{sin^2A}) = cosec^2A(\frac{cos^2A}{sin^2A})$$

= $$cosec^2A(cot^2A)$$

$$\because cosec^2A - cot^2A = 1$$

= $$(cot^2A + 1)cot^2A$$

= $$cot^4A + cot^2A$$

=> Ans - (B)

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