AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0\) then
\(\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=\)
- A \(1\)
- B \(\frac{3}{4}\)
- C \(\frac{9}{16}\)
- D \(\frac{9}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{9}{16}\)
Step-by-step Solution
Detailed explanation
Let \(x=\cos \alpha+i \sin \alpha, y=\cos \beta+i \sin \beta\) and \(z=\cos \gamma+i \sin \gamma \therefore x+y+z=0 \therefore x^3+y^3+z^3=3 x y z\) \(\Rightarrow(\cos \alpha+i \sin \alpha)^3+(\cos \beta+i \sin \beta)^3+(\cos \gamma+i \sin \gamma)^3\)…
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