Question

Based on Pythagorean identities, which equation is true? sine squared theta minus 1 = cosine squared theta secant squared theta minus tangent squared theta = negative 1 negative cosine squared theta minus 1 = negative sine squared theta cotangent squared theta minus cosecant squared theta = negative 1

Answer 1

Answer:

cotangent squared theta minus cosecant squared theta = negative 1.

Step-by-step explanation:

According to Pythagorean theorem, the trigonometric function below is true

Sin²theta + cos²theta = 1 ... (1)

From the equation, if we move cos²theta to the other side, it will become;

Sin²theta = 1-cos²theta

Dividing equation 1 through by cos²theta we will have;

sin²theta/cos²theta + cos²theta/cos²theta = 1/cos²theta

Since sintheta/costheta = tantheta

1/costheta = sec²theta

The equation becomes;

tan²theta + 1 = sec²theta... (2)

Similarly, dividing equation 1 through by sin²theta we will have;

1 + cot²theta = cosec²theta ... (3)

From equation 3, if we move cosec²theta first, we will have;

1 + cot²theta - cosec²theta = 0

Then we move 1 to finally have;

cot²theta - cosec²theta = -1

This shows that only option 4 is true

Answer 2

Answer:

$Cot^2\theta-Csc^2\theta=-1$

Step-by-step explanation:

The only Pythagorean identities are:

$1. \ Sin^2\theta+Cos^2\theta=1$

$2. \ 1+Tan^2\theta=Sec^2\theta$

$3. \ 1+Cot^2\theta=Csc^2\theta$

$4. \ Sin^2\theta=1-Cos^2\theta\\ \ \ Cos^2\theta=1-Sin^2\theta$

 

Therefore,$Cot^2\theta-Csc^2\theta=-1$ is correct as it's one of the pythagorean identities.