Question

PLEASE HELP!

All of the following are Pythagorean Identities EXCEPT:

A. sec^2(x) + 1 = tan^2(x)

B. 1 + cot^2(x) = csc^2(x)

C. sin^2(x) + cos^2(x) = 1

D. tan^2(x) + 1 = sec^2(x)

Answer 1

Answer:

Only A is not Pythagorean Identity.

Step-by-step explanation:

Let us draw a unit circle as shown in the attached figure.

In the given figure, let us apply Pythagorean theorem, which is given by

$x^2+y^2=z^2\\\\x=\sin\theta,y=\cos\theta,z=1\\\\\sin^2\theta+\cos^2\theta=1^2\\\\\sin^2\theta+\cos^2\theta=1........(C)$

Divide both sides by $\sin^2\theta$

$\frac{\sin^2\theta}{\sin^2\theta}+\frac{\cos^2\theta}{\sin^2\theta}=\frac{1}{\sin^2\theta}\\\\1+\cot^2\theta=\csc^2\theta.......(B)$

Divide both side of identity C by  $\sin^2\theta$

$\frac{\sin^2\theta}{\cos^2\theta}+\frac{\cos^2\theta}{\cos^2\theta}=\frac{1}{\cos^2\theta}\\\\\tan^2\theta+1=\sec^2\theta.......(D)$

Therefore, only A is not Pythagorean Identity.