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
Answer (1)
19th Jan, 2024
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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