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Last updated at Feb. 13, 2020 by Teachoo

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Misc 13 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 cosx)/(1 − cos2 x) = tan−1 ((2 cosx)/(sin2 x)) Replacing x with cos x We convert 2tan-1 (cos x) to tan–1 & then equate values Now, Given 2 tan−1 (cos x) = tan−1 (2 cosec x) Putting values tan−1 ((2 cosx)/(sin2 x)) = tan−1 (2 cosec x) (2 cosx)/(sin2 x) = 2 cosec x cosx/(sin2 x) = cosec x cosx/(sin2 x) = 𝟏/(𝐬𝐢𝐧 𝒙) cos x = (sin2 x)/(sin x) [𝑈𝑠𝑖𝑛𝑔 𝑐𝑜𝑠𝑒𝑐 𝑥=1/sin𝑥 ] cos x = sin x 1 = sin𝑥/cos𝑥 sin𝑥/cos𝑥 = 1 tan x = 1 tan x = tan π/4 x = π/4 Hence, x = 𝝅/𝟒 We know that tan 45° = 1 So, tan 𝜋/4 = 1

Formulae based

Inverse Trigonometry Formulas

Example 3 Important

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Misc. 13 Important Not in Syllabus - CBSE Exams 2021 You are here

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.