Question

Which Pythagorean identity is correct?

Answer 1

Answer:

$\tan^2\theta +1 = \sec^2\theta$

True

Option 2 is correct

Step-by-step explanation:

Given:

We need to choose correct option of Pythagorean identity.

Trigonometry formula:

$\tan\theta=\dfrac{P}{B}=\dfrac{1}{\cot\theta}$

$\sin\theta=\dfrac{P}{H}=\dfrac{1}{\csc\theta}$

$\cos\theta=\dfrac{B}{H}=\dfrac{1}{\sec\theta}$

Option 1:

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

$\dfrac{P^2}{H^2}+1=\dfrac{B^2}{H^2}$

$P^2+H^2\neq B^2$

False

Option 2:

$\tan^2\theta +1 = \sec^2\theta$

$\dfrac{P^2}{B^2}+1=\dfrac{H^2}{B^2}$

$\dfrac{H^2}{B^2}=\dfrac{H^2}{B^2}$        $\because B^2+P^2=H^2$

True

Option 3:

$1-\cot^2\theta=\csc^2\theta$

$1-\dfrac{B^2}{P^2}+1=\dfrac{H^2}{P^2}$

$P^2-B^2\neq H^2$

False

Option 4:

$1-\cos^2\theta=\tan^2\theta$

$1-\dfrac{B^2}{H^2}+1=\dfrac{P^2}{B^2}$

$\dfrac{H^2-B^2}{H^2}\neq \dfrac{P^2}{B^2}$

False

Answer 2

The second one. take a right angled triangle and Mark one of the angles as theeta. then take sides as 3,4,5 and put it in options only one of them will satisfy