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Standard Formulae - 3

Find the valu...

Question

Find the value of $x$ :
$s e c^{2} 2 x = 1 - t a n 2 x$

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Solution

$s e c^{2} x = 1 - t a n 2 x 1 + t a n^{2} 2 x = 1 - t a n 2 x o r t a n^{2} 2 x + t a n 2 x = 0 t a n 2 x (t a n 2 x + 1) = 0 i f t a n 2 x = 0 t h e n 2 x = n π o r x = n (\frac{π}{2}) i f t a n 2 x + 1 = 0 o r t a n 2 x = - 1 t a n 2 x = t a n (\frac{- π}{4}) ∴ 2 x = n π + (\frac{- π}{4}) ∴ x = n (\frac{π}{2}) - (\frac{π}{8})$

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