MathematicsIf 2 cosec 2 30 ° +x sin 2 60 ° − 3 4 tan 2 30 ° =10  , then the value of x=[[1]].

If 2 cosec 2 30 ° +x sin 2 60 ° − 3 4 tan 2 30 ° =10  , then the value of x=[[1]].


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    Solution:

    If 2 cosec 2 30 ° +x sin 2 60 ° − 3 4 tan 2 30 ° =10  , then the value of x=3. Given 2 cosec 2 30 ° +x sin 2 60 ° − 3 4 tan 2 30 ° =10  .
    We use the following trigonometric ratios for this question:
    tan 30 ° = 1 3  
    sin 60 ° = 3 2  
    cosec 30 ° =2  
    Putting the values in the equation, we have:
    Simplifying equation (1) to find the value of x, we get:
    ⇒ 3 4 x− 1 4 =10−8 ⇒ 3x−1 4 =2 ⇒3x−1=8  
    ⇒x= 8+1 3 ⇒x= 9 3 ⇒x=3  
    Therefore, the required answer is 3.
     
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