Use the pythagorean identity to do the following:
b. rewrite the expression (1 − cos2(theta)) csc(theta) in terms of a single trigonometric function. state the resulting
identity

2sin(θ)

Step-by-step explanation:       (1 − cos2(theta)) csc(theta)  

cos (2θ) = cos²(θ) - sin²(θ)     ⇒ [(1 - cos²(θ) + sin²(θ)]* csc (θ)

Multiplying        csc(θ) - cos²(θ)*csc(θ) + sin²(θ)*csc(θ)

csc (θ) = 1 ÷ sin (θ)         ⇒   1/sin(θ) - cos²(θ)/sin(θ) + sin²(θ)/sin(θ)

1/sin(θ) [ 1 -cos²(θ) + sin²(θ)]    ⇒  1- cos²(θ) = sin²θ)

1/sin(θ) [ sin²(θ) +sin²(θ) ]

1/sin(θ) [ 2* sin²(θ) ] = 2sin(θ)

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.