If  cos⁡θa=sin⁡θb, then asec⁡2θ+bcosec⁡2θ is equal to

If  cosθa=sinθb, then asec2θ+bcosec2θ is equal to

  1. A

    a

  2. B

    b

  3. C

    ab

  4. D

    a+b

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    Solution:

    We have,

        cosθa=sinθb

    =cosθa=sinθb=cos2θ+sin2θa2+b2b=cosθ=aa2+b2 and sinθ=ba2+b2

         asec2θ+bcosec2θ=acos2θ+bsin2θ

    =  asec2θ+bcosec2θ=acos2θsin2θ+2bsinθcosθ=   asec20+bcosec2θaa2b2a2+b2+2ab2a2+b2=a

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