tan X = cot x

Question

please help me out with this question please

 

Answer 1

 

tan(x) = cot(x)

 

Substitute cot(x) = 1/tan(x)

 

tan(x) = 1/tan(x)

 

tan²(x) = 1

 

tan(x) = ±√1 = ±1

 

x = tan^-1(±1) = 45^o ± n*pi/2, n= 0, 1, 2, 3, ...

Answer 2

tanx = sinx / cosx

 

cotx = cosx / sinx

 

 

(sinx / cosx) = (cosx / sinx)

 

 

Cross multiply.

 

cos²x = sin²x

 

Subtract sin²x on both sides of equation.

 

cos²x - sin²x = 0

 

 

Recall that sin²x + cos²x = 1.  Use this identity to get all trig functions either in terms of sine or cosine.

 

cos²x - (1 - cos²x) = 0

 

cos²x - 1 + cos²x = 0

 

2cos²x - 1 = 0

 

2cos²x = 1

 

cos²x = 1/2

 

 

cos²x is the same as (cosx)².

 

 

cosx = √(1/2)

 

cosx = 1/√2

 

 

Rationalize denominator.

 

 

cosx = √(2) / 2

 

    x = 45