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


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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

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.