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Question:
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Consider the following statements:
1) $\tan ^{-1} 1+\tan ^{-1}(0.5)=\pi / 2$
2) $\sin ^{-1}(1 / 3)+\cos ^{-1}(1 / 3)=\pi / 2$
Which of the above statements is/are correct?
Options:
1) $\tan ^{-1} 1+\tan ^{-1}(0.5)=\pi / 2$
2) $\sin ^{-1}(1 / 3)+\cos ^{-1}(1 / 3)=\pi / 2$
Which of the above statements is/are correct?
Solution:
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Verified Answer
The correct answer is:
2 only
1) L.H.S. $\begin{aligned} \tan ^{-1}(1)+\tan ^{-1}\left(\frac{1}{2}\right) \\=\tan ^{-1}(1)+\cot ^{-1}\left(\frac{1}{\frac{1}{2}}\right) &=\tan ^{-1}+\cot ^{-1} 2 \neq \frac{\pi}{2} \\ \text { So, L.H.S. } \neq \mathrm{RHS} \text { . } \\ \text { 2) } \sin ^{-1} \frac{1}{3}+\cos ^{-1}\left(\frac{1}{3}\right)=\frac{\pi}{2} \\\left\{\sin ^{-1} \mathrm{x}+\cos ^{-1} \mathrm{x}=\frac{\pi}{2}\right\} \end{aligned}$
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