Answer:
[tex]\tan^2\theta +1 = \sec^2\theta[/tex]
True
Option 2 is correct
Step-by-step explanation:
Given:
We need to choose correct option of Pythagorean identity.
Trigonometry formula:
[tex]\tan\theta=\dfrac{P}{B}=\dfrac{1}{\cot\theta}[/tex]
[tex]\sin\theta=\dfrac{P}{H}=\dfrac{1}{\csc\theta}[/tex]
[tex]\cos\theta=\dfrac{B}{H}=\dfrac{1}{\sec\theta}[/tex]
Option 1:
[tex]\sin^2\theta + 1 = \cos^2\theta[/tex]
[tex]\dfrac{P^2}{H^2}+1=\dfrac{B^2}{H^2}[/tex]
[tex]P^2+H^2\neq B^2[/tex]
False
Option 2:
[tex]\tan^2\theta +1 = \sec^2\theta[/tex]
[tex]\dfrac{P^2}{B^2}+1=\dfrac{H^2}{B^2}[/tex]
[tex]\dfrac{H^2}{B^2}=\dfrac{H^2}{B^2}[/tex] [tex]\because B^2+P^2=H^2[/tex]
True
Option 3:
[tex]1-\cot^2\theta=\csc^2\theta[/tex]
[tex]1-\dfrac{B^2}{P^2}+1=\dfrac{H^2}{P^2}[/tex]
[tex]P^2-B^2\neq H^2[/tex]
False
Option 4:
[tex]1-\cos^2\theta=\tan^2\theta[/tex]
[tex]1-\dfrac{B^2}{H^2}+1=\dfrac{P^2}{B^2}[/tex]
[tex]\dfrac{H^2-B^2}{H^2}\neq \dfrac{P^2}{B^2}[/tex]
False
