Question

Based on Pythagorean identities, which equation is true? mc002-1.jpg mc002-2.jpg mc002-3.jpg mc002-4.jpg

Answer 1

Answer:

Cot²θ - csc²θ = -1

Step-by-step explanation:

in right angle triangle

Base²  + Perpendicular² = Hypotenuse²

=> B² + P² = H²

Base/hypotenuse = Cosθ  = B/H

hypotenuse / Base = Secθ  = H/B

Perpendicular /Hypotenuse = Sinθ  = P/H

Hypotenuse/Perpendicular = cscθ  = H/P

Perpendicular / base = Tanθ  = P/B

Base/Perpendicular = Cotθ  = B/P

Sin²θ - 1 = Cos²θ

LHS = (P/H)² - 1  =  (P² - H²)/H² = -B²/H² = -(B/H)² = - Cos²θ ≠ RHS = Cos²θ

Sec²θ - Tan²θ = (H/B)² - (P/B)² = (H² - P²)/B² =  B²/B² = 1 ≠ RHS = -1

-Cos²θ - 1  = - Sin²θ

-Cos²θ - 1  =  - (B/H)² - 1  = - (B² + H²)/H² ≠ RHS

Cot²θ - csc²θ = -1

LHS =  (B/P)² - (H/P)²  = (B² - H²)/P²  = - (H² - B²)/P² = - P²/P² = - 1 = RHS

Cot²θ - csc²θ = -1  equation is true

Answer 2

Answer:

its a on edgenuity

Step-by-step explanation: