AP EAMCET · Maths · Trigonometric Ratios & Identities
In \(\triangle \mathrm{ABC}\), if \(\tan \frac{\mathrm{A}}{2}+\tan \frac{\mathrm{C}}{2}=\frac{\mathrm{b}}{\mathrm{s}}\), then \(\sin \left(\frac{\mathrm{A}+\mathrm{C}}{3}\right)=\)
- A 1
- B \(\frac{\sqrt{3}}{2}\)
- C \(\frac{1}{\sqrt{2}}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\tan \frac{A}{2}+\tan \frac{C}{2}=\frac{b}{s}\) \(\Rightarrow \frac{\sin \frac{A}{2} \cdot \cos \frac{C}{2}+\cos \frac{A}{2} \cdot \sin \frac{C}{2}}{\cos \frac{A}{2} \cdot \cos \frac{C}{2}}=\frac{b}{s}\)…
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