Last updated at Dec. 8, 2016 by Teachoo

Transcript

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)) ∴ "2 tan−1 (cos x)" = tan-1 ((2 cosx)/(sin2 x)) 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) 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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.