General solution of the equation tan 5 x - 5 x is -A- n -20- n - ZB- n -5-20- n - ZC- -5-t-4- n - ZD- n-5- T -20- n - Z

The correct option is D nbsp; n π5±π20, n ∈ℤ nbsp;tan 5x = 5x ⇒tan 5x =1tan 5x ⇒tan^25x=1=tan^2π4 ⇒ 5x = nbsp;n π±π4 ⇒ nbsp; x = nbsp; nbsp; n π5±π ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

General solut...

Question

General solution of the equation $tan 5 x = cot 5 x$ is :

n π \pm \frac{π}{20}, n \in Z

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\frac{n π}{5} + \frac{π}{20}, n \in Z

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\frac{n π}{5} \pm \frac{π}{4}, n \in Z

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\frac{n π}{5} \pm \frac{π}{20}, n \in Z

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Solution

The correct option is D $\frac{n π}{5} \pm \frac{π}{20}, n \in Z$
$tan 5 x = cot 5 x \Rightarrow tan 5 x = \frac{1}{tan 5 x} \Rightarrow {tan}^{2} 5 x = 1 = {tan}^{2} \frac{π}{4} \Rightarrow 5 x = n π \pm \frac{π}{4} \Rightarrow x = \frac{n π}{5} \pm \frac{π}{20}, n \in Z$

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General solution of the equation tan5x=cot5x is :

The correct option is D nπ5±π20, n∈Z tan5x=cot5x⇒tan5x=1tan5x⇒tan25x=1=tan2π4⇒5x=nπ±π4⇒x=nπ5±π20, n∈Z

General solution of the equation $tan 5 x = cot 5 x$ is :

The correct option is D $\frac{n π}{5} \pm \frac{π}{20}, n \in Z$
$tan 5 x = cot 5 x \Rightarrow tan 5 x = \frac{1}{tan 5 x} \Rightarrow {tan}^{2} 5 x = 1 = {tan}^{2} \frac{π}{4} \Rightarrow 5 x = n π \pm \frac{π}{4} \Rightarrow x = \frac{n π}{5} \pm \frac{π}{20}, n \in Z$