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Prove the following identities: (sec-ta...

Prove the following identities: `(sec-tantheta)/(sectheta+tantheta)=1-2secthetatantheta+2tan^2theta`

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To prove the identity \[ \frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta} = 1 - 2 \sec \theta \tan \theta + 2 \tan^2 \theta, \] we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS). ...
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Knowledge Check

  • (sectheta+tantheta-1)(sectheta-tantheta+1)=

    A
    `2 sin theta`
    B
    `2 cos theta`
    C
    `2 sec theta`
    D
    `2 tan theta`

  • (tantheta+sectheta-1)/(tantheta-sectheta+1)=

    A
    `(1-sintheta)/(costheta)`
    B
    `(1+sintheta)/(costheta)`
    C
    `(costheta)/(1-sintheta)`
    D
    `(costheta)/(1+sintheta)`

  • int(sectheta)/(sec theta+tantheta)d theta=

    A
    `tan theta+sectheta+c`
    B
    `-(tan theta+sectheta)+c`
    C
    `tan theta-sectheta+c`
    D
    `sec theta-tan theta+c`

    • Similar Questions

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    sqrt(2)sectheta+tantheta=1

    (tantheta-sectheta)^2

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    Prove the following identities: (1-sin theta)/(1+sin theta)=(sec theta-tan theta)^(2)

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