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प्रश्न
If 2 cos α = `x + 1/x` and 2 cos β = `y + 1/y`, show that `xy - 1/xy = 2"i" sin(alpha + beta)`
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उत्तर
xy = (cos α + i sin α)(cos β + i sin β)
= cos(α + β) + i si(α + β)
∵ arg(z1z2) = arg z1 + arg z2
`1/(xy)` = cos(α + β) – i sin(α + β)
∴ `xy - 1/(xy)` = cos(α + β) + i sin(α + β) – cos(α + β) + i sin(α + β)
= 2i sin(α + β)
Hence proved.
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