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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

$\pm 45^{\circ} + 36^{\circ}$
$\pm 30^{\circ}, \pm 60^{\circ}$
$\pm 75^{\circ}, \pm 36^{\circ}$
$\pm 60^{\circ}, \pm 15^{\circ}$

hint 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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