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Ex 2.2, 9 - Class 12 Inverse CBSE - tan-1 x/root a2 - x2

Ex 2.2, 9 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Ex 2.2, 9 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3


Transcript

Ex 2.2, 9 Write the function in the simplest form: tan-1 𝑥/√(𝑎^2 − 𝑥^2 ) , |x| < a tan-1 𝑥/√(𝑎^2 − 𝑥^2 ) Let x = a sin 𝜽 = tan-1 ((a sin⁡θ)/√(a^2−(a sinθ)^2 )) = tan-1 ((a sin⁡θ)/√(a^2 − a^2 sin2θ)) = tan-1 ((a sin⁡θ)/√(a^2 (1 − sin^2 θ))) = tan-1 ((a sin⁡θ)/(a√(1 − sin^2 θ))) = tan-1 (sin⁡θ/√(cos^2 θ)) We write 𝒙/√(𝒂^𝟐 − 𝒙^𝟐 ) in form of tan Whenever there is √(1 − 𝑥^2 ) we put x = cos θ or sin θ In √(𝒂^𝟐 − 𝒙^𝟐 ) , we put x = a cos θ or a sin θ = tan-1 ((a sin⁡θ)/(a√(1 − sin^2 θ))) = tan-1 (sin⁡θ/√(cos^2 θ)) = tan-1 (sin⁡θ/〖 cos〗⁡θ ) = tan-1 (tan θ) = 𝛉 We assumed that x = a sin θ 𝑥/𝑎 = sin θ sin-1 𝒙/𝒂 = θ Hence, tan-1 𝑥/√(𝑎^2 − 𝑥^2 ) = θ = sin-1 𝒙/𝒂

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.