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Solve for x: 2 tan-1(cosx) = tan-1 (2cosecx) |
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Answer» Given 2 tan-1(cosx) = tan-1 (2cosecx) ⇒ tan-1(2cosx/(1 - cos2x)) = tan-1(2cosecx) [∵ 2tan-1x = tan-1(2x/(1 - x2))] ⇒ tan-1(2cosx/sin2x) = tan-1(2/sinx) ⇒ 2cosx/sin2x = 2/sinx ⇒ cosx/sinx = 1 ⇒ cotx = 1 ⇒ cotx = cotπ/4 ⇒ x = π/4 |
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