Question

the number of solution of equation tan3x =COT4x​

Answer 1

Answer:

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Answer 2

Answer:

There are infinite solutions of given equality.

Step-by-step explanation:

We are given that $tan3x=cot4x$

Solution means the value of angle $x$.

We need to equate them and then solve to find the value of $x$.

We can also write

$\frac{1}{cot3x} =\frac{1}{tan4x}$

$tan4x=cot3x$

Conversion gives

$tan4x=tan(\frac{pi}{2} -3x)$

$tan4x=tan((n pi)\frac{pi}{2} -3x)$

Equating we get

$4x=npi+\frac{pi}{2} -3x$

$4x+3x=npi+\frac{pi}{2}$

$7x=npi+\frac{pi}{2}$

$x=\frac{npi}{7} +\frac{pi}{14}$

Hence, there are infinite solutions.

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