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प्रश्न
If 2 cos α = `x + 1/x` and 2 cos β = `y + 1/y`, show that `x^"m" y^"n" + 1/(x^"m" y^"n")` = 2 cos(mα – nβ)
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उत्तर
= (cos mα + sin mα)(cos nβ + i sin nβ)
= cos(mα + nβ) + i sin(mα + nβ)
`1/(x^"m" y^"n")` = cos(mα + nβ) – i sin(mα + nβ)
∴ `x^"m" y^"n" + 1/(x^"m" y^"n")` = 2 cos(mα – nβ)
Hence proved
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