Question 139

The value of $$\sec^4 A (1 - \sin^4 A) - 2 \tan^2 A$$ is

Solution

$$\sec^4A(1-\sin^4A)-2\tan^2A=\sec^4A-\sec^4A\sin^4A-2\tan^2A$$

$$=\sec^4A-\frac{\sin^4A}{\cos^4A}-2\tan^2A$$

$$=\sec^4A-\tan^4A-2\tan^2A$$

$$=\left(\sec^2A+\tan^2A\right)\left(\sec^2A-\tan^2A\right)-2\tan^2A$$

$$=\left(\sec^2A+\tan^2A\right)\left(1\right)-2\tan^2A$$

$$=\sec^2A+\tan^2A-2\tan^2A$$

$$=\sec^2A-\tan^2A$$

$$=$$ 1

Hence, the correct answer is Option A

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