cot(tetha)=cos(tetha)

Question

so far i have done cos/sin=cos•sin and my teacher told me to equal it to zero but i i'm stuck. can someone help me find q1 2 3 4 

Answer 1

Let x = theta

 

cot(x) = cos(x)

 

 

The identity cot(x) = cos(x) / sin(x).

 

(cos(x) / sin(x) = cos(x)

 

 

Subtract cos(x) on both sides of equation.

 

(cos(x) / sin(x)) - cos(x) = 0

 

 

The LCD is sin(x).

 

(cos(x) - cos(x)sin(x)) /sin(x) = 0

 

 

cos(x) - cos(x)sin(x) = 0

 

cos(x)(1 - sin(x)) = 0

 

 

Set the factors equal to zero.

 

cos(x) = 0           and           1 - sin(x) = 0

                                               sin(x) = 1

 

x = π/2                                        x = π/2

x = 3π/2                                      

 

 

The solutions are

 

x = π/2

x = 3π/2

 

Answer 2

The equation reduces to 1/sin = sin. The only way that can be equal is if theta = pi/2.

Answer 3

hi .. can u elaborate the question