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prove that- sin^2theta/cos^2theta+cos^2...

prove that- `sin^2theta/cos^2theta+cos^2theta/sin^2theta=1/ (sin^2thetacos^2theta)-2`

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sin^4theta+2sin^2thetacos^2theta=1-cos^4 theta

cos theta+sin theta=cos2 theta+sin2 theta

Knowledge Check

  • (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta) =

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

  • The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^(4)theta cos^(2)theta+cos^(6)theta sin^(2)theta+3sin^(2)thetacos^(4)theta is equal to

    A
    `cos^(2)2 theta`
    B
    `sin^(2)2theta`
    C
    `cos^(3)2 theta+sin^(3)2theta`
    D
    none of these

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    Prove the following identities: 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)+1=0sin^(6)theta+cos^(6)theta+3sin^(2)theta cos^(2)theta=1(sin^(8)theta-cos^(8)theta)=(sin^(2)theta-cos^(2)theta)(1-2sin^(2)theta cos^(2)theta)

    (sin3 theta+cos3 theta)/(cos theta-sin theta)=1+2xx sin2 theta

    sin theta+sin2 theta+sin3 theta=1+cos theta+cos2 theta

    Prove the following identity: ((1)/(sec^(2)theta-cos^(2)theta)+(1)/(cos ec^(2)theta-sin^(2)theta))sin^(2)theta cos^(2)theta=(1-sin^(2)theta cos^(2)theta)/(2+sin^(2)cos^(2)theta)

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