MHT CET · Maths · Trigonometric Ratios & Identities
The value of \(\tan \left(\frac{\pi}{8}\right)\) is
- A \(\sqrt{2}-1\)
- B \(1-\sqrt{2}\)
- C \(\sqrt{2}\)
- D \(\sqrt{2}+1\)
Answer & Solution
Correct Answer
(A) \(\sqrt{2}-1\)
Step-by-step Solution
Detailed explanation
Since, \(\tan \frac{A}{2}=\frac{1-\cos A}{\sin A}\) Putting \(\frac{\mathrm{A}}{2}=\frac{\pi}{8}\), we get
\(\tan \left(\frac{\pi}{8}\right) =\frac{1-\cos \frac{\pi}{4}}{\sin \frac{\pi}{4}} \)
\( =\frac{1-\frac{1}{\sqrt{2}}}{\left(\frac{1}{\sqrt{2}}\right)} \)
\( \therefore \tan \left(\frac{\pi}{8}\right) =\sqrt{2}-1\)
\(\tan \left(\frac{\pi}{8}\right) =\frac{1-\cos \frac{\pi}{4}}{\sin \frac{\pi}{4}} \)
\( =\frac{1-\frac{1}{\sqrt{2}}}{\left(\frac{1}{\sqrt{2}}\right)} \)
\( \therefore \tan \left(\frac{\pi}{8}\right) =\sqrt{2}-1\)
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