MathematicsFind the value of x from the following equation cosec π 2 +θ +xcosθcot π 2 +θ =sin π 2 +θ  .

Find the value of x from the following equation cosec π 2 +θ +xcosθcot π 2 +θ =sin π 2 +θ  .


  1. A
    0
  2. B
    sinθ  
  3. C
    cosθ  
  4. D
    tanθ  

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    Solution:

    Let the given equation be cosec π 2 +θ +xcosθcot π 2 +θ =sin π 2 +θ  .
    We know that, sin π 2 +θ =cosθ,cot π 2 +θ =tanθ,cosec π 2 +θ =secθ  .
    Substitute the above values in the equation, and we have
    secθ+xcosθ(tanθ)=cosθ secθxcosθtanθ=cosθ  
    We know that, sec= 1 cosθ ,tanθ= sinθ cosθ  .
    1 cosθ xcosθ sinθ cosθ =cosθ 1 cosθ xsinθ=cosθ xsinθ= 1 cosθ cosθ xsinθ= 1 cos 2 θ cosθ  
    We know that, sin 2 θ=1 cos 2 θ  .
    xsinθ= sin 2 θ cosθ x= sinθ cosθ x=tanθ  
    Hence, the correct option is 4.
     
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