Question

Verify the trigonometric identity:

(1 + tan^2x) cos^2x = 1

Answer 1

Okay... remember the identity... \(1 + \tan ^2 x = \)____

Answer 2

Can you tell me what comes in the blank?

Answer 3

It doesn't look right to me

Answer 4

See.. we have...

\(1 + \tan^2 x = \sec^2 x\)

And what is \(\sec x\) in terms of \(\cos x\) ?

Answer 5

cos(2x) = cos^2(x) -sin^2(x)

Answer 6

Looks like OP is offline... anyways I will give the final hint...

\(\sec x = \cfrac{1}{\cos x}\)

Using this and the identity I mentioned earlier you can get the answer

Answer 7

@daniel.ohearn1
It is cosine squared x

Answer 8

(1+tan^2 x)cos^2 x = 1

(1+sin^2 x/cos^2 x )cos^2 x = 1

((cos^2 x +sin^2 x)/cos^2 x)cos^2 x = 1

(1/cos^2 x)cos^2 x = 1

1=1