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Question
`(tan^3θ - 1)/(tanθ - 1)` = sec2θ + tanθ
Solution
डावी बाजू = `(tan^3θ - 1)/(tanθ - 1) = (tan^3θ - 1^3)/(tanθ - 1)`
= `((tanθ - 1)(tan^2θ + tanθ + 1))/((tanθ - 1))` ......…[∵ a3 – b3 = (a - b) (a2 + ab + b2)]
= tan2θ + tan θ + 1
= (1 + tan2θ) + tan θ
= sec2θ + tan θ ......…[∵ 1 + tan2θ = sec2θ]
= उजवी बाजू
∴ `(tan^3θ - 1)/(tanθ - 1)` = sec2θ + tanθ
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