Question

Which of the following is NOT a valid Pythagorean identity?cos2θ+sin2θ=1cosine squared theta plus sine squared theta is equal to 1cos2θ=1−sin2θcosine squared theta is equal to 1 minus sine squared theta1+tan2θ=sec2θ1 plus tangent squared theta is equal to secant squared thetasec2θ+tan2θ=1secant squared theta plus tangent squared theta is equal to 1

Answer 1

sec²θ + tan²θ = 1

Step-by-step explanation

The main Pythagorean identity is,

`\cos^2\theta+\sin^2\theta=1`

If we subtract sin²θ from both sides, we obtain the second option given,

`\begin{gathered} \cos^(2)\theta+\sin^(2)\theta-\sin^(2)\theta=1-\sin^(2)\theta \\ \\ \cos^2\theta=1-\sin^2\theta \end{gathered}`

And, if we divide both sides by cos²θ, we obtain the third option given,

`\begin{gathered} (\cos^2\theta+\sin^2\theta)/(\cos^2\theta)=(1)/(\cos^2\theta) \\ \\ 1+\tan^2\theta=\sec^2\theta \end{gathered}`

Hence, the last option, sec²θ + tan²θ = 1 is not a valid Pythagorean identity.