Question

Which identity needs to be used to prove tan (pi/2 - x) = cot x

Answer 1

The answer is tanФ = sinФ/cosФ ⇒ the second answer

Explanation:

∵ tanx = sinx/cosx , ∵ cotx = cosx/sinx

∵ tan(π/2 - x) =
`(sin(\pi )/(2)-x )/(cos(\pi )/(2)-x )`

∵ sin(π/2 - x) = cosx ⇒ complementary angles (sum of them = π/2)

∵ cos(π/2 - x) = sinx

∴ tan(π/2 - x) =
`(cosx)/(sinx)` = cotx

∴ The identity is tanФ = sinФ/cosФ