Question 46

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

Solution

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Expression : $$(sec^4A - tan^2A) - (tan^4A + sec^2A)$$

= $$(sec^4A-tan^4A)+(-sec^2A-tan^2A)$$

= $$[(sec^2A+tan^2A)(sec^2A-tan^2A)]+(-sec^2A-tan^2A)$$

Using, $$(sec^2A-tan^2A=1)$$

= $$(sec^2A-sec^2A)+(tan^2A-tan^2A)=0$$

=> Ans - (C)

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