tanA/(1+tan^2 A)^2+cotA/(1+cot^2 A)^2=sinA.cosA

Asked by  | 29th Aug, 2012, 09:27: PM

Expert Answer:

tanA/(1+tan^2 A)^2+cotA/(1+cot^2 A)^2
= tanA/(sec^2 A)^2+cotA/(cosec^2 A)^2
= tanA/(sec^4 A)+cotA/(cosec^4 A)
= sinA/(sec^3 A)+cosA/(cosec^3 A)
= cosec^2 A + sec^2 A/sec^3 A cosec^3 A
= 1/sin^2 A + 1/cos^2 A/sec^3 A cosec^3 A
= 1/sin^2 Acos^2 A/sec^3 A cosec^3 A
= 1/secA cosec A
= sinA cosA

Answered by  | 29th Aug, 2012, 10:40: PM

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