Question 46

What is the simplified value of $$(cosec^4 A - cot^2 A) - (cot^4 A + cosec^2 A)?$$

Solution

Expression : $$(cosec^4 A - cot^2 A) - (cot^4 A + cosec^2 A)$$

= $$(cosec^4A-cot^4A)+(-cosec^2A-cot^2A)$$

= $$[(cosec^2A+cot^2A)(cosec^2A-cot^2A)]+(-cosec^2A-cot^2A)$$

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

= $$(cosec^2A-cosec^2A)+(cot^2A-cot^2A)=0$$

=> Ans - (A)

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