What is the simplified value of $$cosec^6A - cot^6A - 3 cosec^2A cot^2A$$ ?
Expression :Â $$cosec^6A - cot^6A - 3 cosec^2A cot^2A$$
= $$(cosec^2A)^3-(cot^2A)^3-3(cosec^2A)(cot^2A)(1)$$
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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