# tan(2x-5) - cot(x+1) = 0?

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- 4 years agoFavourite answer
sin(2x - 5) / cos(2x - 5) - cos(x + 1) / sin(x + 1) = 0

sin(2x - 5) / cos(2x - 5) = cos(x + 1) / sin(x + 1)

sin(2x - 5) * sin(x + 1) = cos(2x - 5) * cos(x + 1)

0 = cos(2x - 5) * cos(x + 1) - sin(2x - 5) * sin(x + 1)

0 = cos((2x - 5) + (x + 1))

0 = cos(2x + x - 5 + 1)

0 = cos(3x - 4)

If x is in degrees

cos(3x - 4) = 0

3x - 4 = 90 + 180 * k

k is an integer

3x = 94 + 180 * k

x = 94/3 + 60 * k

x = 31.333333.... + 60 * k

x = 31.333.... , 91.333.... , 151.333.... , 211.333... , 271.333.... , 331.333.....

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