prove the identity tanx+cotx=secxcscx?

3 Answers

Relevance
  • 9 years ago
    Favorite Answer

    work from left side

    sinx/cosx + cosx/sinx

    common denominator

    sin²x/(sinx cosx) + cos²x/(sinx cosx)

    (sin²x + cos²x)/(sinx cosx)

    Use identity that

    (sin²x + cos²x) = 1

    You have

    1/(sinx cosx)

    Split apart

    1/sinx * 1/cosx

    Or

    1/cosx * 1/sinx

    secx * cscx

    • Login to reply the answers
  • 9 years ago

    tanx + cotx = sinx/cosx + cosx/sinx = (sin²x + cos²x)/(sinx cosx) =

    1/(sinx cosx) = secx cscx

    • Login to reply the answers
  • 9 years ago

    tan x = sin x / cos x

    cot x = 1/tan x = cos x /sin x

    So, tan x + cot x = (sin x/cos x) + (cos x/sin x) = (sin^2 x + cos^2 x)/(sin x cos x)

    sin^2 x + cos ^ x = 1

    So, tan x + cot x = 1/(sin x cos x)

    sec x = 1/cos x

    csc x = 1/sin x

    So, sec x csc x = (1/cos x)(1/sin x) = 1/(cos x sin x)

    • Login to reply the answers
Still have questions? Get your answers by asking now.