JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(\cot \alpha=1\) and \(\sec \beta=-\frac{5}{3}\), where \(\pi<\alpha<\frac{3 \pi}{2}\) and \(\frac{\pi}{2}<\beta<\pi\), then the value of \(\tan (\alpha+\beta)\) and the quadrant in which \(\alpha+\beta\) lies, respectively are
- A \(-\frac{1}{7}\) and \(IV\) \(^{\text {th }}\) quadrant
- B \(7\) and \(I ^{ st }\) quadrant
- C \(-7\) and \(IV\) \(^{\text {th }}\) quadrant
- D \(\frac{1}{7}\) and \(I ^{ st }\) quadrant
Answer & Solution
Correct Answer
(A) \(-\frac{1}{7}\) and \(IV\) \(^{\text {th }}\) quadrant
Step-by-step Solution
Detailed explanation
\(\cot \alpha=1, \sec \beta=\frac{-5}{3}, \cos \beta=\frac{-3}{5}, \tan \beta=\frac{-4}{3}\) \(\tan (\alpha+\beta)=\frac{1-\frac{4}{3}}{1+\frac{4}{3} \times 1}=\frac{-1}{7}\)
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