Ask Question
24 August, 10:43

Verify the identity. cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent of x

+4
Answers (1)
  1. 24 August, 13:33
    0
    We are asked to verify the function: cot x / (1+cscx) = (cscx-1) / cotx that is to simplify each side of the equation to be equal to each other. In this case, we can use the trigonometric identities to determine if both sides are equal to each other.

    cot x = 1/tan x

    tan x = sinx / cosx

    Ergo, cot x = cos x / sinx

    cscx = 1/sinx

    left side: cotx / (1 + csc x) = cos x / sinx / (1+1/sinx) = cosx / (sinx + 1) * sinx/sinx = cosx / (sinx + 1)

    Right side: (cscx-1) / cotx = ((1/sinx) - 1) * sinx/cosx = (1-sinx) * sinx/sinx*cosx =

    1-sinx / cosx

    using a calculator, these two are equal.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Verify the identity. cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers