Math

posted by .

How can I prove this identity?

(1 + sinØ + cosØ):(1 - sinØ + cosØ) =
(1 + sinØ) : cosØ

  • Math -

    Work on the left hand side:
    (1 + sinØ + cosØ)/(1 - sinØ + cosØ)
    multiply both the numerator and denominator by (1-sinφ+cosφ) and simplify:
    ((1+cosφ)^2-sin&hi;^2)/(1-sinφ+cosφ)^2
    =2cosφ(1+cosφ)/[2(1-sinφ)(1+cosφ)]
    =2cosφ/[2(1-sinφ)]
    =cosφ/(1-sinφ)
    Now multiply top and bottom by (1+sinφ)
    cosφ(1+sinφ)/(1-sin²φ)
    =cosφ(1+sinφ)/cos²φ
    =(1+sinφ)/cosφ

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. trig

    how do you solve this problem? 1+sinØ/cosØ +cosØ/1+sinØ = 2secØ and cosß- cosß/1-tanß = sinßcosß/sinß-cosß
  2. Algebra 2

    As the answer to: (tanØ * cosØ/ sinØ) + cotØ * sinØ * tanØ* cscØ I got 2, is that correct?
  3. maths

    if sinØ=cosØ then find the value of Ø
  4. math

    Two sides of a triangle have lengths 8 m and 24 m. The angle between them is increasing at a rate of 0.05 rad/s. Find the rate at which the area of the triangle is changing when the angle between the sides of fixed length is 135°. …
  5. Advanced Functions/Precalculus

    1. The expression sinπ is equal to 0, while the expression 1/cscπ is undefined. Why is sinø=1/cscø still an identity?
  6. Trig

    Prove the following: 1/(tanØ - secØ ) + 1/(tanØ + secØ) = -2tanØ (1 - sinØ)/(1 + sinØ) = sec^2Ø - 2secØtanØ + tan^2Ø
  7. Algebra 2

    Verify the identity , justify each step tanØ+cotØ = 1/ sin Ø cosØ
  8. Math

    If cscØ = 4/3, find sinØ + sinØ cot^2 Ø
  9. Math

    If cscØ = 4/3, find sinØ + sinØ cot^2 Ø
  10. Maths

    Prove that:Tanø+sinø/tanø-sinø=secø+1/secø-1

More Similar Questions