Question

What is the solution? ABCD
please give some explanation

Answer 1

`\cos(x) ( \tan(x) - √(3) ) = 0`

`\cos(x) ( ( \sin(x) )/( \cos(x) ) - √(3) ) = \\`

Thus :

`\cos(x) = 0 \: \: \: or \: \: \: \tan(x) - √(3) = 0`

Over interval [0 , 2pie ) :

`\cos(x) = 0`

`x = (\pi)/(2) , (3\pi)/(2) \\`

And

`\tan(x) - √(3) = 0`

`\tan(x) = √(3)`

`x = (\pi)/(3) ,\pi + (\pi)/(3) \\`

`x = (\pi)/(3) , (4\pi)/(3) \\`

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Thus the solutions are :

`(\pi)/(3) , (\pi)/(2) , (4\pi)/(3) , (3\pi)/(2) \\`

As u can see the first option is the correct answer .

And we're done....

Have a great day ♡♡♡♡♡