Misc. 2 - Chapter 2 Class 12 Inverse Trigonometric Functions

Transcript

Misc 2 Find the value of tan−1(tan⁡〖7π/6〗 ) Let y = tan−1(tan⁡〖7π/6〗 ) tan y =〖 tan〗⁡〖7π/6〗 tan y = tan (210°) We know that range of principal value of tan-1 is ("−" 𝜋/2 " , " 𝜋/2) i.e. (−90° ,90°) Hence y = 210° not possible Now, tan y = tan (210°) tan y = tan (180° + 30°) tan y = tan (30°) tan y = tan (30 × 𝜋/180) tan y = tan (𝜋/6) Hence, y = 𝜋/6 Which is in the range of principal value of tan-1 i.e. ((−π)/2, π/2) Hence, tan–1(tan⁡〖3π/4〗 ) = y = 𝝅/𝟔 (As tan (180 + θ) = tan θ)