Question

Which Pythagorean identity is correct?

Answer 1

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

Answer 2

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

True

Option 2 is correct

Explanation:

Given:

We need to choose correct option of Pythagorean identity.

Trigonometry formula:

`\tan\theta=(P)/(B)=(1)/(\cot\theta)`

`\sin\theta=(P)/(H)=(1)/(\csc\theta)`

`\cos\theta=(B)/(H)=(1)/(\sec\theta)`

Option 1:

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

`(P^2)/(H^2)+1=(B^2)/(H^2)`

`P^2+H^2\\eq B^2`

False

Option 2:

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

`(P^2)/(B^2)+1=(H^2)/(B^2)`

`(H^2)/(B^2)=(H^2)/(B^2)`
`\because B^2+P^2=H^2`

True

Option 3:

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

`1-(B^2)/(P^2)+1=(H^2)/(P^2)`

`P^2-B^2\\eq H^2`

False

Option 4:

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

`1-(B^2)/(H^2)+1=(P^2)/(B^2)`

`(H^2-B^2)/(H^2)\\eq (P^2)/(B^2)`

False