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General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

Write the gen...

Question

Write the general solution of $t a n^{2} 2 x = 1.$

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Solution

$t a n^{2} 2 x = 1 \Rightarrow t a n^{2} 2 x - 1 \Rightarrow (t a n 2 x - 1) (t a n 2 x + 1) = 0 \Rightarrow t a n 2 x = 1 o r t a n 2 x = - 1 \Rightarrow t a n 2 x = t a n \frac{π}{4} O r t a n 2 x = - t a n (\frac{π}{4}) = t a n (π - \frac{π}{4}) = t a n (\frac{3 π}{4}) 2 x = x π + \frac{π}{4} O r 2 x = x π + \frac{3 π}{4}, x \in z \Rightarrow x = \frac{x π}{2} + \frac{π}{8} o r x = \frac{x π}{2} + \frac{3 π}{8} \Rightarrow x = \frac{x π}{2} + \frac{π}{8}, x \in z$

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