Maths-
General
Easy

Question

If 3 Tan to the power of 4 space alpha minus 10 Tan squared space alpha plus 3 equals 0 then principal values of ' alpha ' are

  1. plus-or-minus 45 to the power of ring operator plus 36 to the power of ring operator
  2. plus-or-minus 30 to the power of ring operator comma plus-or-minus 60 to the power of ring operator
  3. plus-or-minus 75 to the power of ring operator comma plus-or-minus 36 to the power of ring operator
  4. plus-or-minus 60 to the power of ring operator comma plus-or-minus 15 to the power of ring operator

Hint:

In this question, we have to find the value of alpha in the equation 3 tan squared alpha minus 10 tan squared alpha plus 3 equals 0. For this we will make the trigonometric identity of both the sides equal, then we will equate the sides to get the value of alpha.

The correct answer is: plus-or-minus 30 to the power of ring operator comma plus-or-minus 60 to the power of ring operator


    space space space space 3 t an to the power of 4 space alpha minus 10 t an squared space alpha plus 3 equals 0
rightwards double arrow 3 t an to the power of 4 space alpha minus 9 tan squared alpha minus t an squared space alpha plus 3 equals 0
rightwards double arrow 3 space tan squared alpha left parenthesis tan squared alpha minus 3 right parenthesis minus 1 left parenthesis tan squared alpha minus 3 right parenthesis equals 0
rightwards double arrow left parenthesis 3 space tan squared alpha minus 1 right parenthesis left parenthesis tan squared alpha minus 3 right parenthesis equals 0
rightwards double arrow tan squared alpha equals 1 third o r space tan squared alpha equals 3
rightwards double arrow tan alpha equals fraction numerator 1 over denominator square root of 3 end fraction o r space tan space alpha equals square root of 3
rightwards double arrow tan space alpha equals tan space left parenthesis plus-or-minus 30 degree right parenthesis o r space tan space left parenthesis plus-or-minus 60 degree right parenthesis
rightwards double arrow alpha space equals space plus-or-minus 30 degree space o r space plus-or-minus 60 degree

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