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Maths-

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Question

e number of solutions of the equation $tan invisible function application x plus sec invisible function application x minus 2 cos invisible function application x$ lying in the interval $left square bracket 0 comma blank 2 pi right square bracket$ is

0
1
2
3

The correct answer is: 2

The given equation is
$tan invisible function application x plus sec invisible function application x equals 2 cos invisible function application x$
$rightwards double arrow fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction plus fraction numerator 1 over denominator cos invisible function application x end fraction equals 2 cos invisible function application x$
$rightwards double arrow sin invisible function application x plus 1 equals 2 cos to the power of 2 end exponent invisible function application x equals 2 minus 2 sin to the power of 2 end exponent invisible function application x$
$rightwards double arrow 2 sin to the power of 2 end exponent invisible function application x plus sin invisible function application x minus 1 equals 0$
$rightwards double arrow open parentheses 2 sin invisible function application x minus 1 close parentheses open parentheses sin invisible function application x plus 1 close parentheses equals 0$
$rightwards double arrow sin invisible function application x equals fraction numerator 1 over denominator 2 end fraction comma blank minus 1$
$rightwards double arrow x equals fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction comma fraction numerator 3 pi over denominator 2 end fraction element of left square bracket 0 comma blank 2 pi right square bracket$
But for $x equals 3 pi divided by 2$ , $tan invisible function application x$ and $sec invisible function application x$ are not defined
Therefore, there are only two solutions

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$i s blank e q u a l blank t o$

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