Question 94

What is the simplified value of $$cosec^6A - cot^6A - 3 cosec^2A cot^2A$$ ?

Solution

Expression : $$cosec^6A - cot^6A - 3 cosec^2A cot^2A$$

= $$(cosec^2A)^3-(cot^2A)^3-3(cosec^2A)(cot^2A)(1)$$

Using, $$(cosec^2A-cot^2A=1)$$

= $$(cosec^2A)^3-(cot^2A)^3-3(cosec^2A)(cot^2A)(cosec^2A-cot^2A)$$

Using, $$x^3-y^3-3xy(x-y)=(x-y)^3$$

= $$(cosec^2A-cot^2A)^3$$

= $$(1)^3=1$$

=> Ans - (D)

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