Answer the following?

Question

Answer 1

This is not a question about Chemistry.  It needs moving to Mathematics.

Answer 2

1+cot²θ = csc²θ

cot²θ = csc²θ - 1

tan²θ = 1/(csc²θ - 1)

tanθ = - √[1/(csc²θ - 1)]     .... negative root is selected as θ belongs to QII

tanθ = - √[1/((9/4)² - 1)]

tanθ = - √[1/(81/16) - 1)]

tanθ = - √[1/(65/16)]

tanθ = - √(16/65)

tanθ = - 4/√65

cosθ = (cosθ/sinθ)*sinθ

cosθ = (1/tanθ)(1/cscθ)

cosθ = -((√65)/4)(4/9)

cosθ = -(√65)/9