Math, asked by deremon, 1 day ago

tan8x=cot2x solve this​

Answers

Answered by brainly2107
0

Answer:

tan 8x = cot 2x

=> cot (90-8x) = cot 2x

=> 90-8x = 2x

=> 90 = 2x+8x

=> 90 = 10x

=> x = 90/10

=> x = 9

Answered by Manmohan04
0

Given,

\[\tan 8x = \cot 2x\]

Solution,

\[\begin{array}{l}\tan 8x = \cot 2x\\ \Rightarrow \frac{{\sin 8x}}{{\cos 8x}} = \frac{{\cos 2x}}{{\sin 2x}}\\ \Rightarrow \sin 8x\sin 2x = \cos 8x\cos 2x\\ \Rightarrow \cos 8x\cos 2x - \sin 8x\sin 2x = 0\\ \Rightarrow \cos \left( {8x + 2x} \right) = 0\\ \Rightarrow \cos 10x = \cos \frac{\pi }{2}\end{array}\]

Simplify it,

\[\begin{array}{l} \Rightarrow 10x = \frac{\pi }{2}\\ \Rightarrow x = \frac{\pi }{{20}}\end{array}\]

Hence the value of x is \[\frac{\pi }{{20}}\].

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