# Prove the cofunction Identity using the Addition and Subtraction Formulas. Tan (pi/2 - u) = cot (u) Since tan (pi/2) is undefined, use a Reciprocal Identity, and then use the Substitution Formulas to simplify. Tan (pi/2 - u) = sin/cos (pi/2 - u) = (cos (u)) - (cos (pi/2)) (sin (u))/(sod (pi/2)) (cos (u)) + (sin (pi/2)) (sin (u)) = (cos (u)) - (0) (sin (u))/(0) (cos (u)) + (1) (sin (u)) =/sin (u)

1 answer

###### Question:

Prove the cofunction Identity using the Addition and Subtraction Formulas. Tan (pi/2 - u) = cot (u) Since tan (pi/2) is undefined, use a Reciprocal Identity, and then use the Substitution Formulas to simplify. Tan (pi/2 - u) = sin/cos (pi/2 - u) = (cos (u)) - (cos (pi/2)) (sin (u))/(sod (pi/2)) (cos (u)) + (sin (pi/2)) (sin (u)) = (cos (u)) - (0) (sin (u))/(0) (cos (u)) + (1) (sin (u)) =/sin (u)

## Answers

Answer:Step-by-step explanation:We are to prove the cofunction Identity using the Addition and Subtraction Formulas. [tex]tan(\pi/2 - u) = cot (u)[/tex]From trigonometry identity, [tex]tan x = sinx/cosx[/tex], starting from right hand side of the equation, the expression above will become;[tex]tan(\pi/2 - u) = \dfrac{sin(\frac{\pi}{2}-u )}{cos(\frac{\pi}{2}-u) }........ \ 1 \\\\from\ quadrant;\\\\sin(\frac{\pi}{2}-u) = cos (u) \ and \ cos(\frac{\pi}{2}-u) = sin(u)[/tex]Substituting this trigonometry identities into equation 1 we will have;[tex]tan(\pi/2 - u) = \dfrac{cos(u)}{sin(u)}[/tex]Since cot(u) = 1/tan(u) = cos(u)/sin(u), hence;[tex]tan(\pi/2 - u) = \dfrac{cos(u)}{sin(u)} = cot(u)\\\\tan(\pi/2 - u) = cot (u)\ Proved![/tex]

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