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प्रश्न
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
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उत्तर
The given equation is cot θ = `sqrt(3)` which is same as tan θ = `1/sqrt(3)`.
We know that,
tan `π/6 = 1/sqrt(3)` and tan(π + θ) = tan θ
∴ `tan π/6 = tan(π + π/6) = tan (7π)/(6)`
∴ `tan π/6 = tan (7π)/6 = 1/sqrt(3)`, where
`0 < π/6 < 2π and 0 < (7π)/6 < 2π`
∴ cot θ = `sqrt(3)`, i.e. tan θ = `1/sqrt(3)` gives
tan θ = `tan π/6 = tan (7π)/6`
∴ θ = `π/6 and θ = (7π)/6`
Hence, the required principal solutions are θ = `π/6 and θ = (7π)/6`.
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