Verify the identity by working down one side of the identity

Verify the identity by working down one side of the identity or the other, or both sides of the identity.

cos³(t)+sin³(t)=[1-sin(t)cos(t)] [sin(t)+cos(t)]

Solution

cos³t + sin³t

We have to use the following formula

a³+b³=(a+b)(a²-ab+b²)

(cos t + sin t)(cos²t-sint cos t +sin²t)

(cos t + sin t)(1-sint cos t) which is equal to right side .