Verify the identity.

(1 + tan^2u)(1 - sin^2u) = 1

Question

Verify the identity.

(1 + tan^2u)(1 - sin^2u) = 1

anonymous · Answer

tan^2u = (sin^2u)/(cos^2u)
sin^2u + cos^2u = 1

now what can you do with the above?

anonymous · Answer

i'm not sure.

anonymous · Answer

from:
sin^2u + cos^2u = 1
you get:
cos^2u = 1 - sin^2u

how about now?

anonymous · Answer

i'm sorry i just don't understand this.

anonymous · Answer

so you know the following identities:
tan^2u = (sin^2u)/(cos^2u)
cos^2u = 1 - sin^2u

substitute the above accordingly to the equation:
(1 + tan^2u)(1 - sin^2u) = (1 + (sin^2u)/(cos^2u))(cos^2u)  
                                     = cos^2u + cos^2u[ (sin^2u)/(cos^2u)]
                                     = cos^2u + sin^2u
                                     =?

anonymous · Answer

$$(1+\frac{ \sin^2x }{ \cos^2x })(\cos^2x)=1$$$$\cos^2x+\sin^2x=1$$

anonymous · Answer

@ChmE How did you skip to that last step? I don't understand it, and I don't think the asker would either, can you please clarify?

anonymous · Answer

distributed cos^2(x) to each term