AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\sin ^3 10^{\circ}+\sin ^3 50^{\circ}-\sin ^3 70^{\circ}=\)
- A \(\frac{-3}{8}\)
- B \(\frac{3}{4}\)
- C \(\frac{\sqrt{3}}{2}\)
- D \(\frac{-1}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{-3}{8}\)
Step-by-step Solution
Detailed explanation
Apply the identity \(\sin^3 x + \sin^3(60^{\circ}-x) - \sin^3(60^{\circ}+x) = -\frac{3}{4}\sin 3x\). Substitute \(x=10^{\circ}\): \(\sin ^3 10^{\circ}+\sin ^3 (60^{\circ}-10^{\circ})-\sin ^3 (60^{\circ}+10^{\circ}) = -\frac{3}{4}\sin (3 \times 10^{\circ})\).…
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