Solve for x: tan x + cot x = 1

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The trigonometric equation tan x + cot x = 1 has to be solved for x.

tan x + cot x = 1

Let tan x = y

=> y + 1/y = 1

=> y^2 + 1 = y

=> y^2 - y + 1 = 0

Here b^2 - 4ac = (-1)^2 - 4*1*1 = -3 which is negative. The equation derived has complex roots. tan x can only take on real values. As a result it is not possible to determine the value of x.

The given quadratic equation has no roots.

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vaaruni | High School Teacher | (Level 1) Salutatorian

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Given : tan x + cot x = 1 => (sin x)/(cos x) + (cos x/sin x) =1 => (sin^2 x + cos^2 x)/(sin x.cos x)= 1 => 1/(sin x.cos x) = 1 [since, sin^2 x+cos^2 x) =1 ] => 1/(2sin x.cos x) = 1/2 [ dividing both sides by 2] => 1/sin(2x) = 1/2 => sin(2x) = 2 This equation has no solution because maximum value of sin of any angle is equal to 1

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