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Check whether the following equations ar...

Check whether the following equations are identities or not ?
(i) `(costheta)/(1-sintheta)=(1+sintheta)/(costheta)`
(ii) `(1)/(1+costheta)+(1)/(1-costheta)=2"cosec"^(2)theta`
(iii)`(sin^(2)theta)/(1-sin^(2)theta)=(1)/(3)`
(iv) `sin^(2)theta+cos^(2)theta=1`
(v) `(1+costheta-sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta`
(vi) `1+(tan^(2)theta)/(1+sectheta)=sectheta`

Text Solution

Verified by Experts

The correct Answer is:
(i),(ii),(iv),(v),(vi) are identities
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Prove that : (1+costheta- sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta

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Knowledge Check

  • (sintheta+sin2theta)/(1+costheta+cos2theta) =

    A
    `(1)/(2)tantheta`
    B
    `(1)/(2)cottheta`
    C
    `tantheta`
    D
    `cottheta`

  • (sintheta+sin2theta)/(1+costheta+cos2theta)=?

    A
    `tantheta`
    B
    `sintheta`
    C
    `costheta`
    D
    `tan^(2)theta`

  • (sin3theta-cos3theta)/(sintheta+costheta)+1 =

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

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    Explore conceptually related problems

    (sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

    ("sin"theta)/(1-costheta)+("tan"theta)/(1+costheta)=secthetacosectheta+cottheta

    (sin^(3)theta+cos^(3)theta)/(sintheta+costheta)+(sin^(3)theta-cos^(3)theta)/(sintheta-costheta)=

    (sin^(2)theta)/(costheta(1+costheta))+(1+costheta)/(costheta)=?

    If (cos^(2)theta)/(1-tantheta)+(sin^(3)theta)/(sintheta-costheta)=K+sinthetacostheta , then K = ?

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