Question : The simplest value of $\sin^{2}x+2\tan^{2}x-2\sec^{2}x+\cos^{2}x$ is:
Option 1: 1
Option 2: 0
Option 3: –1
Option 4: 2
Correct Answer: –1
Solution : Given: $\sin^{2}x+2\tan^{2}x-2\sec^{2}x+\cos^{2}x$ We know that, $\sec^2x=\tan^2x+1$ and $\sin^2x+\cos^2x=1$ Putting the values, we get: = $\sin^{2}x+2\tan^{2}x-2(\tan^2x+1)+\cos^{2}x$ = $\sin^{2}x+\cos^{2}x+2\tan^{2}x-2\tan^2x-2$ = $1-2$ = $-1$ Hence, the correct answer is –1.
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