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प्रश्न
The general solution of the equation tan θ tan 2θ = 1 is given by ______
पर्याय
`(2n + 1)pi/6,` n ∈ I
`npi + pi/6`, n ∈ I
`npi - pi/6`, n ∈ I
`npi ± pi/6`, n ∈ I
MCQ
रिकाम्या जागा भरा
उत्तर
The general solution of the equation tan θ tan 2θ = 1 is given by `underline(npi ± pi/6, n ∈ I`.
Explanation:
tan θ tan 2θ = 1
∴ `tantheta (2tantheta)/(1 - tan^2theta) = 1`
∴ `2tan^2theta = 1 - tan^2theta`
∴ `3tan^2theta = 1`
∴ `tan^2theta = 1/3 = tan^2(pi/6)`
∴ `theta = npi ± pi/6` ..........[∵ tan2θ - tan2α ⇒ θ = nπ ± α]
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Trigonometric Equations and Their Solutions
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