Verify the identity. Show your work.

(1 + tan2u)(1 - sin2u) = 1

Question

11-06-2016
Mathematics

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Verify the identity. Show your work.

(1 + tan2u)(1 - sin2u) = 1

Respuesta :

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georgiatrn georgiatrn · Answer 1 · 2016-06-12T11:03:39+02:00

I assume you mean (1 + tan^2u)(1 - sin^2u) = 1 so I solved it like that

because tanu = sinu / cosu ⇒ tan^2u = sin^2u / con^2u

(1 + sin^2u/cos^2u)(1 - sin^2u) =
(cos^2u/cos^2u + sin^2u/cos^2u)(1 - sin^2u) =
((cos^2u + sin^2u)/(cos^2u)) (1 - sin^2u) =

and because cos^2u + sin^2u = 1 we'll have

(1/(cos^2u)) (1 - sin^2u) =
1/(cos^2u) - sin^2u/(cos^2u) =
(1 - sin^2u) / (cos^2u) =

notice that 1 - sin^2u is equal to cos^2u

cos^2u / cos^2u = 1

Verify the identity. Show your work. (1 + tan2u)(1 - sin2u) = 1

Respuesta :

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Verify the identity. Show your work.

(1 + tan2u)(1 - sin2u) = 1