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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 2.2, 7 Write the function in the simplest form: tan−1 ((3a2x −x3)/(a3 −3ax2)), α > 0; (−a)/√3 ≤ x ≤ a/√3 tan−1 ((3a2x − x3)/(a3 − 3ax2)) Putting x = a tan θ = tan−1 ((3a^2 (a tan θ) − (a tan θ)^3)/(a^3 − 3a (a tan θ)^2 )) = tan−1 ((3a^3 tan θ − a^3 tan^3 θ)/(a^3 − 3 a.a^2 tan^2 θ)) = tan−1 ((a^3 (3 tan θ − tan^3 θ))/(a^3 (1 − 3 tan^2 θ))) = tan−1 ((3 tan θ − tan^3 θ)/(1 − 3tan^2 θ)) = tan−1 (tan 3θ) = 3θ We know x = a tan θ 𝑥/𝑎 = tan θ tan θ = 𝑥/𝑎 θ = tan−1 (𝒙/𝒂) Hence, tan−1 ((3a2x − x3)/(a3 − 3ax2)) = 3θ = 3 tan−1 𝒙/𝒂 Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.