TS EAMCET · Maths · Inverse Trigonometric Functions
\(\text { If } \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}\)
then \(1-x y-y z-z x\) is equal to
- A 1
- B 0
- C -1
- D 2
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
\(\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}\) \(\Rightarrow\left(\tan ^{-1} x+\tan ^{-1} y\right)+\tan ^{-1} z=\frac{\pi}{2}\) \(\Rightarrow \tan ^{-1}\left(\frac{x+y}{1-x y}\right)+\tan ^{-1} z=\frac{\pi}{2}\)…
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