MathematicsIf sinα= 1 2   and cosβ= 1 2 ,   then which of the following is the measure of the angle (α+β)  ?

If sinα= 1 2   and cosβ= 1 2 ,   then which of the following is the measure of the angle (α+β)  ?


  1. A
    25 °  
  2. B
    35 °  
  3. C
    40 °  
  4. D
    90 °   

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    Solution:

    The given trigonometric ratios are,
    sinα= 1 2   and cosβ= 1 2  
    Therefore we have,
    sinα= 1 2  
    sinα=sin 30 °   α= 30 °  
    Also,
      cosβ= 1 2   cosβ=cos 60 °   β= 60 °   Thus,
    α+β= 30 ° + 60 °   α+β= 90 °  
    Therefore, the measure of the angle (α+β)= 90 ° .  
    Hence, option (4) is correct.
     
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