JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
For \(\alpha, \beta, \gamma \neq 0\). If \(\sin ^{-1} \alpha+\sin ^{-1} \beta+\sin ^{-1} \gamma=\pi\) and \((\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3 \alpha \beta\), then \(\gamma\) equal to
- A \(\frac{\sqrt{3}}{2}\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{\sqrt{3}-1}{2 \sqrt{2}}\)
- D \(\sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{3}}{2}\)
Step-by-step Solution
Detailed explanation
\(\text { Let } \sin ^{-1} \alpha=A, \sin ^{-1} \beta=\mathrm{B}, \sin ^{-1} \gamma=\mathrm{C}\) \(\mathrm{A}+\mathrm{B}+\mathrm{C}=\pi\) \((\alpha+\beta)^2-\gamma^2=3 \alpha \beta\) \(\alpha^2+\beta^2-\gamma^2=\alpha \beta\)…
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