Question

Which statements are true based on Pythagorean identities

Answer 1

Check all of the available options
⇒ First option sin²α = 1 + cos²α
    Use first pythagorean identity to solve whether the equation is true
    (Solve for sin²α)
    sin²α + cos²α = 1
    sin²α = 1 - cos²α
    The result is different from the first option, so the first option is not valid

⇒ Second option 1 = sec²α - tan²α
    Use second pythagorean identity (solve for 1)
    tan²α + 1 = sec²α
    1 = sec²α - tan²α
    The result is the same, thus the second option is valid

⇒ Third option cot²α = csc²α - 1
    Use third pythagorean identity (solve for cot²α)
    1 + cot²α = csc²α
    cot²α = csc²α - 1
    The result is the same, thus the third option is valid

⇒ Fourth option 1 - tan²α = -sec²α
    Use second pythagorean identity
    tan²α + 1 = sec²α (multiply by -1)
    -tan²α - 1 = -sec²α
    -1 - tan²α = -sec²α
    The result is different from the option, so the fourth option is not valid

⇒ Fifth option -cos²α = sin²α - 1
    Use first pythagorean identity
    sin²α + cos²α = 1
    cos²α = 1 - sin²α (multiply by -1)
   -cos²α = -1 + sin²α
   -cos²α = sin²α - 1
   The result is the same, thus the fifth option is valid

ANSWER: second, third, fifth option

Answer 2

Answer:

If the second, third, or fifth option doesn't work, pick all of them

Step-by-step explanation:

I just did it