Solve tan 2x - - x- -3

Step 1: Simplification Given: tan2x = ( x+ π3 ) ⇒tan2x = tan nbsp; ( π2 + x+ nbsp; π3 ) ⇒tan2x = tan nbsp; ( 3 π + 2 π6 + x ) ⇒tan2x = tan nbsp; ( 5 ...

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Standard XII

Physics

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

Standard XII Physics

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Solve tan2x=−cot(x+π3)

Step 1: Simplification Given: tan2x=−cot(x+π3) ⇒tan2x=tan(π2+x+π3) ⇒tan2x=tan(3π+2π6+x) ⇒tan2x=tan(5π6+x) Step 2: General solution ⇒2x=nπ+x+5π6 ⇒x=nπ+5π6 ∴ General solution is x=nπ+5π6, where n∈Z

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