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Definite Integrals

Solve tan 2x ...

Question

Solve $tan 2 x = - cot (x + \frac{π}{3})$

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Solution

Step $1 :$ Simplification
Given: $tan 2 x = - cot (x + \frac{π}{3})$
$\Rightarrow tan 2 x = tan (\frac{π}{2} + x + \frac{π}{3})$
$\Rightarrow tan 2 x = tan (\frac{3 π + 2 π}{6} + x)$
$\Rightarrow tan 2 x = tan (\frac{5 π}{6} + x)$

Step 2: General solution
$\Rightarrow 2 x = n π + x + \frac{5 π}{6}$
$\Rightarrow x = n π + \frac{5 π}{6}$

$∴$ General solution is $x = n π + \frac{5 π}{6},$ where $n \in Z$

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Definite Integrals

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