I am working on Trig Identities... I need help proving something true:?

Question

The problem is :

cos^2x + tan^2x * cos^2x = 1

I have tried and tried... I can not seem to figure this one out! Any suggestions would be appreciated, please and thanks! :-)

Answer 1

To prove: cos^2x + tan^2x * cos^2x =? 1

tan = sin / cos
tan^2 = sin^2 / cos^2
tan^2 * cos^2 = sin^2
Therefore,
cos^2 + tan^2 * cos^2 = cos^2 + sin^2
But this is known to = 1
QED

Answer 2

I haven't done real trig for 25 years, but let's give this a try:
tan x = (sin x / cos x), right?

Thus
cos^2x + tan^2x * cos^2x = 1

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

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

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

Giving:

cos^2x + sin ^2 x * = 1 Because (cos^2 x / cos^2 x) cancels.

The result is true - it's a rule. It's because it's a restatement of Pythagoras for the unit circle; the hypotenuse is the radius of the unit circle is 1 ( = 1^2), the cos is the adjacent and the sin is the opposite at right angles. (Pythagoras applies to right-angle triangles. a^2 + b^2 = c^2 )

Answer 3

=cos^2x+(tan^2x*cos^2x)
=cos^2x+{(sin^2x/cos^2x) * cos^2x} // tan a=sin a/ cos a
=cos^2x+{sin^2x} // cos^2x gets cancelled by cos^2x
=cos^2x+sin^2x // After opening curly brackets
=1 // cos^a + sin^a=1;it is a trig. identity
HENCE PROVED

Answer 4

= cos²x + (sin²x / cos²x).cos²x
= cos²x + sin²x
= 1 as required

Answer 5

tan^2x = sin^2x/cos^2x

so cos^2x +sin^2x *cos^2x/cos^2x = (simplify by sin^2x)

cos^2x+sin^2x =1

Answer 6

tanx^2 = sinx^2/cosx^2 so
sinx^2/cosx^2 * cosx^2 = sinx^2


this right here is a trig identity.
cosx^2 + sinx^2 = 1

Answer 7

Never took trig but I am working too............on my tan