MathematicsIf cotθ= 15 8 ,   then evaluate (2+2sinθ)(1−sinθ) (1+cosθ)(2−2cosθ)  .

If cotθ= 15 8 ,   then evaluate (2+2sinθ)(1sinθ) (1+cosθ)(22cosθ)  .


  1. A
    225 64  
  2. B
    15 8  
  3. C
    75 16  
  4. D
    75 8   

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    Solution:

    Given that cotθ= 15 8  .
    The trigonometric function cotθ= base perpendicular   .
    Let us denote hypotenuse by H, base by B and perpendicular by P.
    sinθ= P H ,cosθ= B H    According to Pythagoras theorem,
      H 2 = P 2 + B 2 cotθ= B P = 15 8    It becomes,
    H 2 = (15) 2 + (8) 2 H 2 =225+64 H 2 =289 H=17  
    Now,
    sinθ= P H sinθ= 8 17 cosθ= B H cosθ= 15 17  
    Now the expression (2+2sinθ)(1sinθ) (1+cosθ)(22cosθ   can be simplified as,
    Hence the value of (2+2sinθ)(1sinθ) (1+cosθ)(22cosθ)  is 225 64  .
    Therefore option 1 is correct.
     
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