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Prove that: (sintheta+cosectheta)^(2)+...

Prove that:
`(sintheta+cosectheta)^(2)+(costheta+sectheta)^(2)` =7+`tan^(2)theta+cot^(2)theta`

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Prove that (1+cot theta - cosec theta)(1+tan theta + sec theta) =2 .

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Knowledge Check

  • If thetain(0,pi/2) , then the value of : |((sintheta+"cosec"theta)^2,(sintheta-"cosec"theta)^2,1),((costheta+sectheta)^2,(costheta-sectheta)^2,1),((tantheta+cottheta)^2,(tantheta-cottheta)^2,1)|=

    A
    `sin theta +costheta+tantheta`
    B
    1
    C
    0
    D
    4

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    Prove that ((1+cos theta)/(1-cos theta))=("cosec"theta + "cot"theta)^(2)

    Prove that cosec^(2) theta + sec^(2) theta = cosec^(2) theta sec^(2) theta .

    Show that, cot theta.costheta +sin theta = cosec theta

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

    Prove that (sec theta + tan theta)^(2) = (cosec theta +1)/(cosec theta -1) .

    Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

    Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

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