[JEE Advanced 1978] Express $\dfrac1{1-\cos\theta+2i\sin\theta}$ in the form $x+iy$.
Express $\dfrac1{1-\cos\theta+2i\sin\theta}$ in the form $x+iy$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Answer: $x=\dfrac1{5+3\cos\theta},\quad y=\dfrac{-2\sin\theta}{(1-\cos\theta)(5+3\cos\theta)}$.
Multiply by the conjugate: $|\text{den}|^2=(1-\cos\theta)^2+4\sin^2\theta=(1-\cos\theta)(5+3\cos\theta)$. Then $x=\frac{1-\cos\theta}{(1-\cos\theta)(5+3\cos\theta)}=\frac1{5+3\cos\theta}$ and $y=\frac{-2\sin\theta}{(1-\cos\theta)(5+3\cos\theta)}$.
JEE Advanced 1978 · Complex Numbers — verified solution by the Vidaara Team.
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