Question

solve tanx+cotx=1....,.......

Answer 1

The Given Question is Wrong
or the Given Question has no Solutions

There are various ways to prove that the question is wrong

I will use the following method to prove that question is wrong


=> tanx + cotx =1
=> sinx/cosx + cosx/sinx =1;
=> (sin²x + cos²x)/sinx×cosx =1
=> 1/(sinx×cosx) =1   =>    sinx×cosx=1
=> 2sinx×cosx=2
=>sin 2x = 2

Since the Range of Sine Function is -1≤sin x≤1
The above condition is not possible

Answer 2

tanx + cotx = 1
⇒sinx/cosx + cosx/sinx = 1
⇒(sin²x + cos²x )/simx.cosx = 1
we know,
Sin²Ф + cos²Ф = 1
⇒1/simx.cosx = 1
⇒2/2sinx.cosx = 1
we know, 2simФ.cosФ = sin2Ф
⇒2/sin2x = 1
⇒sin2x = 2 , but sinx ∈ [ -1, 1]
So, equation is wrong it's not possible.



√2cosθ + 1 = 0
⇒ √2cosθ = -1
⇒cosθ = -1/√2
According to Trigonometry equation
Cosθ = cosα , then, θ = 2nπ ± α
So, θ = 2nπ ± cos⁻¹(-1/√2)