WBJEE · Maths · Inverse Trigonometric Functions
Value of \(\tan ^{-1}\left(\frac{\sin 2-1}{\cos 2}\right)\) is
- A \(\frac{\pi}{2}-1\)
- B \(1-\frac{\pi}{4}\)
- C \(2-\frac{\pi}{2}\)
- D \(\frac{\pi}{4}-1\)
Answer & Solution
Correct Answer
(B) \(1-\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
Hints : \(\tan ^{-1}\left(\frac{\sin 2-1}{\cos 2}\right)=\tan ^{-1}\left(\frac{-(\sin 1-\cos 1)^2}{(\cos 1-\sin 1)(\cos 1+\sin 1)}\right) \quad=-\tan ^{-1}\left(\frac{\cos 1-\sin 1}{\cos 1+\sin 1}\right)=1-\frac{\pi}{4}\)
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