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tanA-cot-A-2cosec2A-




Question Number 9414 by Rohit kumar last updated on 06/Dec/16
tanA+cot=A= 2cosec2A
$${tanA}+{cot}={A}=\:\mathrm{2}{cosec}\mathrm{2}{A} \\ $$
Answered by ridwan balatif last updated on 06/Dec/16
tanA+cotA=2cosec2A  ((sinA)/(cosA))+((cosA)/(sinA))=2cosec2A  ((sin^2 A+cos^2 A)/(cosA×sinA))=2cosec2A  (1/((1/2)×(2cosA×sinA)))=2cosec2A  (2/(sin2A))=2cosec2A  2cosec2A=2cosec2A
$$\mathrm{tanA}+\mathrm{cotA}=\mathrm{2cosec2A} \\ $$$$\frac{\mathrm{sinA}}{\mathrm{cosA}}+\frac{\mathrm{cosA}}{\mathrm{sinA}}=\mathrm{2cosec2A} \\ $$$$\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{A}+\mathrm{cos}^{\mathrm{2}} \mathrm{A}}{\mathrm{cosA}×\mathrm{sinA}}=\mathrm{2cosec2A} \\ $$$$\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{2cosA}×\mathrm{sinA}\right)}=\mathrm{2cosec2A} \\ $$$$\frac{\mathrm{2}}{\mathrm{sin2A}}=\mathrm{2cosec2A} \\ $$$$\mathrm{2cosec2A}=\mathrm{2cosec2A} \\ $$

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