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Prove that : (tan^(2)theta)/(1+tan^(2...

Prove that : `(tan^(2)theta)/(1+tan^(2)theta)+(cot^(2)theta)/(1+cot^(2)theta)=1`

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Prove that : (tan^(3) theta)/(1+tan^(2)theta) +(cot^(3)theta)/(1+cot^(2)theta) = sec theta "cosec " theta - 2 sin theta cos theta .

(1-cot^(2)theta)/(tan^(2)theta-1)=cot^(2)theta

Knowledge Check

  • If sin 2theta=k , then the value of (tan^(3)theta)/(1+tan^(2)theta)+(cot^(3)theta)/(1+cot^(2)theta) is equal to

    A
    `(1-k^(2))/(k)`
    B
    `(2-k^(2))/(k)`
    C
    `k^(2)+1`
    D
    `2-k^(2)`

  • Let f(theta)=(tan^(3)theta)/(1+tan^(2)theta)-(cot^(3)theta)/(1+cot^(2)theta), 0 lt theta lt (pi)/(4) . Then f(theta) is equal to

    A
    `tan theta +cot theta`
    B
    `2sin(2theta)`
    C
    `-2cot(2theta)`
    D
    0

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    Prove that (tan^(3)theta)/(1+tan^(2)theta)+(cot^(3)theta)/(1+cot^(2)theta)=sec theta cos ec theta-2sin theta cos theta

    Prove each of the following identities : (tan^(2) theta)/((1+ tan^(2) theta)) + (cot^(2) theta)/((1+ cot^(2) theta)) =1

    Prove that : (1-tan^(2)theta)/(cot^(2)theta-1)=tan^(2)theta

    Prove: (tan^(3)theta)/(1+tan^(2)theta)+(cot^(3)theta)/(1+cot^(2)theta)=sec theta cos ec theta-2sin theta cos theta

    If 3cot theta=4 then show that (1-tan^(2)theta)/(1+tan^(2)theta)=(cos^(2)theta-sin^(2)theta)

    Prove each of the following identities : (tan theta)/((1+ tan^(2) theta)^(2)) + (cot theta)/((1+ cot^(2) theta)^(2)) = sin theta cos theta

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