Misc 11 - Chapter 2 Class 12 Inverse Trigonometric Functions

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Misc 11 Solve 2 tan−1 (cos x) = tan−1 (2 cosec x) Solving 2tan−1 (cos x) We know that "2 tan−1 x = tan−1 " 𝟐𝐱/(𝟏 − 𝐱^𝟐 ) "2 tan−1 (cos x)" = tan−1 (2 cos⁡x)/(1 − cos2 x) = tan−1 ((𝟐 𝐜𝐨𝐬⁡𝐱)/(𝐬𝐢𝐧𝟐 𝐱)) Now, Given 2 tan−1 (cos x) = tan−1 (2 cosec x) Putting values tan−1 ((𝟐 𝐜𝐨𝐬⁡𝐱)/(𝐬𝐢𝐧𝟐 𝐱)) = tan−1 (2 cosec x) (2 cos⁡x)/(sin2 x) = 2 cosec x cos⁡x/(sin2 x) = cosec x cos⁡x/(sin2 x) = 𝟏/(𝐬𝐢𝐧 𝒙) cos x = (sin2 x)/(sin x) cos x = sin x 1 = sin⁡𝑥/cos⁡𝑥 sin⁡𝑥/cos⁡𝑥 = 1 tan x = 1 tan x = tan π/4 x = π/4 Hence, x = 𝝅/𝟒

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo