Step 1:

Alternating  sinusoidal current is .

Where, is amplitude, is the time and  is the phase.

For alternating current, the differential amount of heat  by joule-lenz law is .

Find the quantity of heat released by alternating sinusoidal current during a cycle in a conductor by integrating above expression.

.

Substitute in above expression.

Double angle  identity: .

Step 2:

Therefore, heat released by alternating sinusoidal current during a cycle in a conductor is .

Solution:

Heat released by alternating sinusoidal current during a cycle in a conductor is .

Consider .

Rewrite the expression as .

Trigonometric property: .

Again use trigonometric property: .

.

Hence