Solve: tan5X = cot 2X Please try solving asap. Thank you:)
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You should move `cot 2x` to the left side such that:
`tan 5x - cot 2x = 0 `
You may write `cot 2x = tan(pi/2 - 2x)` such that:
`tan 5x - tan(pi/2 - 2x) = 0 `
You need to convert the difference into a product such that:
`(sin(5x - pi/2 + 2x))/(cos 5x cos (pi/2 - 2x)) = 0 `
The fraction is equal to zero if `sin(7x - pi/2) = 0` and `(cos 5x cos (pi/2 - 2x)) != 0` such that:
`sin(7x - pi/2) = 0 => 7x - pi/2 = (-1)^n arcsin 0 + npi`
`7x - pi/2 = npi => 7x = npi + pi/2 => x = npi/7 + pi/14`
Hence, evaluating the general solution to the given equation yields `x = npi/7 + pi/14.`
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tan5x=cot2x
=>sin5x/cos5x=cos2x/sin2x
=> cos2x cos5x = sin2x sin5x
=> cos2x cos5x - sin2x sin5x = 0
=> cos(2x+5x)=0
=> cos 7x =0
=> cos 7x= cos 90
=> 7x= 90
=> x= 90/7
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