Find the principal solution(s) of $s e c x s i n^{2} x = t a n x$

$x = 0$

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$x = \frac{π}{4}$

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$x = \frac{π}{2}$

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$x = π$

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Solution

The correct option is A
$x = 0$

$s e c x s i n^{2} x = t a n x \frac{s i n x}{c o s x} s i n x = t a n x t a n x s i n x = t a n x t a n x = 0 o r s i n x = 1 x = 0 o r x = \frac{π}{2}$
But sec x and tan x are not defined at $x = \frac{π}{2}$
Therefore, x = 0 is the only solution.

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