Question

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

Answer 1

hi @highschoolmom2010,
what have you tried,
there are several ways using trigonometric identities in which you can prove this.

One of the easier ways, i can think of is using:
\(1+\tan^2x = \sec^2 x \\ \sin^2x +\cos^2 x = 1 \\ \sec x \cos x = 1\)
with these 3 identities, that will be easily proved.

Answer 2

You will get a workout on trig identies with this problem:

(1 + tan^2u) = sec ² u

(1 - sin^2u) = cos ² u


sec ² u and cos ² u are reciprocal trig functions


Putting this together:


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

sec ² u * cos ² u = 1

See if this makes sense: @highschoolmom2010

1 = 1

@