Question

If \(\sec\theta+\tan\theta+1=0\), then the value of \(\sec\theta-\tan\theta\) is

• A. \(1\)
• B. \(-1\)
• C. \(0\)
• D. \(2\)

Hint:

Products \((\sec\pm\tan)(\sec\mp\tan)=1\) are handy consequences of \(\sec^{2}-\tan^{2}=1\).

Answer 1

The Correct Option is B

Step 1: Use \(\sec^{2}\theta-\tan^{2}\theta=1\).
\((\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=1\).
Step 2: Substitute the given value.
\(\sec\theta+\tan\theta=-1\Rightarrow \sec\theta-\tan\theta=\dfrac{1}{-1}=-1\).