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Prove the following trigonometric identi...

Prove the following trigonometric identities: `(sintheta)/(1-costheta)=cos e ctheta+cottheta`

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Given,
`(sintheta)/(1-costheta)`
`=(sintheta)/(1-costheta)xx(1+costheta)/(1+costheta)`
`=((sintheta)(1+costheta))/(1-cos^2theta)`
`=((sintheta)(1+costheta))/(sin^2theta)`
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Knowledge Check

  • (sintheta + cos theta)(tan theta + cottheta) =

    A
    1
    B
    `sintheta.costheta`
    C
    `sectheta."cosec"theta`
    D
    `sectheta+"cosec"theta`

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    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

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